1. Give an example of a logarithmic equation that cannot be solved and explain why it cannot be solved

2. Describe how you would verify the solutions to a logarithmic equation.

3. Is it possible to use the quotient law to evaluate log -7/4? Explain.

4. Describe the steps for solving log₂ (x+2)=log₂15

5. Is the following statement true? Explain why or why not. log ( − 3 ) + log ( − 4 ) = log ⁡ ( 12 )

Seems like it would be a sensible way of stating the real perceived brightness of any light source unlike the current units that really don't convey the diminishing returns.

If you have seen the following questions before, please do not post the answers, but of course you can join the discussion after the answers are revealed. We’ll try to post at least one fresh graph weekly until March 21, whether basic or complex, each graph uses GAMSAT-level reasoning.

Of course, calculators and rulers are not permitted. If you are new to these types of problems, don’t time yourself; if this is common fare for you, you have 90 seconds per question.

If you want to submit a hidden response so others continue in suspense, put tags around your answer

>! Like this !<

and it will show up like this >! Hello !<

Caution ahead. Good luck!

GAMSAT Graph Analysis Unit 8

In microbiology, a colony-forming unit (CFU) is a unit used to estimate the number of viable bacterial cells in a sample.

Consider the following diagram.

Figure 1 Comparison of the time-kill curves of bacteria incubated in the presence of various antimicrobials (‘A’ means the antimicrobial alone).

Question 1

According to Figure 1, the largest drop in the number of viable bacterial cells per mL, between hour 1 and hour 10, occurs with which of the following trials?

A Antimicrobial alone

B Antagonist

C Additive

D Synergistic

Question 2

At hour 6 in Figure 1, which of the following best approximates the difference in viable bacterial cell numbers per mL between the trial with the Control and the trial with Antimicrobial alone?

A 1000

B 100 000

C 10 000 000

D 1 000 000 000

Question 3

Based on Figure 1, the fastest increase in the numbers of viable bacterial count per mL per hour occurs in the ‘Control’ group between which of the following time periods?

A Hour 0 and 0.5

B Hour 0 and 2

C Hour 2 and 3

D Hour 3 and 4

Past posts:

• Unit 1
• Unit 2
• Unit 3
• Unit 4
• [Unit 5](https://www.reddit.com/r/GAMSAT/comments/ewuzz9/gamsat_graphs_unit_5_problembased_learning/

I imagine a lot of people like me have already bought the SP200 as there were some really good sales out there but for those of you considering it and havent pulled the trigger yet please read!

The production SP200 has a linear potentiometer which means it raises volume at a constant rate rather than gradually increasing at first then having larger increases towards the end of the potentiometer. Given how ridiculous its power output is, this is a MAJOR flaw. It is going to be TOO much power for a lot of headphones out there. It also has some channel balance issues below 9-10 o clock and even that is a ton of power in low gain. Getting to the point where the channels are balanced is impossible for anything sensitive.

My Onkyo A800 is 32ohms with 100db sensitivity, so pretty sensitive (and I cant even get past 7 o clock without it being absurdly loud. This amp is just not usable with a lot of headphones without having a preamp of some kind to cut the volume (and you need to cut it by quite a bit! Even with a -5db preamp EQ setting I couldnt get past 9 with the A800)!

So if you are considering the SP200 be sure to get a DAC like the SU-8 that has volume control or its only going to be suitable for really insensitive headphones.

microMathematics Plus (μMath+ for short) — FOSS extended visual calculator.

Main developer: /u/mkulesh

CHANGELOG:

• Implemented SI units of information
• Expanded image settings: now it is now possible to use an automatic color adjustment for SVG images depending on application theme
• Changed app icon in order to support Android Oreo icon shape
• For a function plot, it is now possible to use logarithmic scale

Documentation (PDF): https://github.com/mkulesh/microMathematics/raw/supplement/doc/microMathematics-v2.17.2.pdf

You could grab APK from:

• F-Droid: https://f-droid.org/packages/com.mkulesh.micromath.plus
• GitHub: https://github.com/mkulesh/microMathematics/releases/tag/v2.17.2
• Google Play: https://play.google.com/store/apps/details?id=com.mkulesh.micromath.plus

Nio is down nearly 40% this year. I manage almost $250K worth of shares and call options so the pain is REAL. Can't afford the double-doubles anymore, have to buy singles w/ no drinks :(

So with that disclaimer, here's why NIO is a buy at this $28-30 range, aka now.

1. Marketing/Strategy: The Nio team have been textbook perfect in their execution.-It's paramount that an early stage startup targets and monopolizes a niche market of "non-consumers" before taking on the world. In the vein, Nio targeted the luxury EV market segment in China.

-Furthermore, within the luxury Chinese EV niche, they targeted busy salarymen/women that couldn't afford to wait 30-minutes for a turbo-charge. A sub-10-minute battery swap addresses this market segment's need to replenish charge on the go. Furthermore, with cute ai-robots, passenger massage chairs, and a dealership that feels more like a country club, Nio has distinguished itself in its domestic market from non-native competitors like Tesla and BMW. This tightly controlled distribution strategy allows Nio to scale up safely while improving cash flow before they expand to new markets.-Nio then smartly targeted the Norwegian market, which has the highest per capita market share of EV's in the world. At Nio Day, they had Alan Walker (Norwegian musician) to headline the event.-Also at Nio Day, they revealed an expansion plan that includes most of Europe and the United States.

Net Result: Nio was able to hit 100K car deliveries in half the time it took Tesla (12-years), despite the chip shortage, factory shutdowns from the pandemic, and skyrocketing competition from incumbent players (We must still thank the almighty Tesla for being the pioneer, and on another post, I might outline why VW and GM will likely fail to take significant market share in the EV market).

2. Pricepoint-Consumers of internal combustion engine (ICE) vehicles have been conditioned to allocate a monthly budget to pay for gas, oil changes, and maintenance fees. Nio offers a subscription fee to lease the battery, which is the most expensive component of an EV. Not paying for the battery up front dramatically reduces the cost of the vehicle, expanding customer acquisition, and also increases the lifetime value (LTV) of each customer. A luxury car like the ET5 can cost just $40K (comparable to the Model 3 or a BMW 3-Series), yet those same customers will be paying Nio's subscription fees for years and become loyal customers over time.

3. **Par

In high school I was taught that “log” without a specified base referred to a base 10, and that “natural log” or “ln” referred to a base e.

In the last week two professors of mine independently wrote “ln” to refer to a log of base-e, and then corrected themselves to writing “log” instead. Is “natural log” old fashioned? Should “log” with an unspecified base be assumed to mean log base-e?

Hi all, as a hobby over the past few months I've put together a free scientific calculator app with some cool features (and ad free, no internet permission requested at all!). Available at:

• Android (Google Play): https://play.google.com/store/apps/details?id=net.alexbarry.calc_android
• Web version, good on mobile or desktop: https://alexbarry.github.io/AlexCalc/

Some cool features:

• nicely formatted LaTeX equation display, no more counting brackets to determine if you correctly entered your input
• complex number support, in rectangular or polar form (e.g. 3 + 4i or 1 angle 90)
• variable storage (e.g. 123 -> x then 3*x^2 - 4*x + 5 -> y)
• units in equations, and conversion (e.g. 1 inch * 3 ft to cm^2 or sqrt(60 acre) - 100 ft (defaults to SI units, metres in this case))
• can enter input by button presses, typing, or copy/pasting. Button presses are all converted to plaintext input for easy copy/pasting.
• equation display is simplified upon pressing enter. This means that when entering an equation, it is usually possible to look only at the LaTeX display and not the plaintext input: but when pressing enter, it will look nice. Redundant brackets are removed, including those that are needed for plaintext input (e.g. (a + b)/(c + d) can become "a + b" on the numerator and "c + d" on the denominator without brackets).
• light/dark themes (on android, see note [0] below for web)
• previous input history can be accessed and edited by pressing "up" or "down" buttons.
• previous inputs/vars/recently used units preserved when the (android) app is closed. (see note [0] below for web)
• standard scientific calculator features, such as:
  • trigonometric functions: sin, cos, tan, arcsin, arccos, arctan
  • base 10 and natural logarithmic functions: log (base 10), ln (base e)
  • e, pi constants, and square root function
  • scientific notation input (e.g. 1.23E6 is 1.23 times 10^6)

I made this because many years ago when I was in school, I wanted a calculator app with some of these features (specifically entering complex polar numbers in degrees), and I wanted the same app available on my phone or computer. Unfortunately I and all my friends are out of school now, so I don't have much of a use for it.

Some technical details:

• core calculator code is written in C++ and I use JNI (native) in android. (Compiled to WASM for the web version)
• LaTeX equation display uses MathJax in a webview.

Also I'm happ

I've been thinking about this for a while. I understand that if: y = a ^ x then the inverse is x = log_a (y). But what I want to know is what that relationship represents. If I were to graph both functions, how can I interpret the values of the logarithmic function (as I understand, the exponential function represents exponential growth)? And how the values returned by the function in the same value X are related to each other? Hope this makes sense. Thanks in advance!

It's hard to imagine exponentiation, logs, and roots as continuous operators, but clearly they must be. Is it possible to get units this weird? And what would they mean?

Introduction

For most of us, the charts we are most familiar with are in linear space (also known as arithmetic space). Linear space is the default chart space for just about any exchange or price tracking app. This is because linear space is the chart space that essentially all people are most comfortable with and accustomed to.

You may have noticed that many exchanges and apps have an option on their charts called Log or Logarithmic Space. If you don't know what logarithmic space is or how it differs from linear space (or even what linear space is), then this post is for you.

In addition to explaining logarithmic space, I will try to convince you that log space is a critical tool for understanding the market, because it provides insights (especially on large timescales) that can not be easily observed in linear space.

Linear Space

In order to understand the shortcomings of linear space, consider the following chart.

https://preview.redd.it/1z4u2eq2qv681.png?width=1526&format=png&auto=webp&s=7fc30c2d04069870c11039eb4cd4437a976df56a

This is a chart of the entire history of Bitcoin price since 2010 until present, in linear space. Most of you will have heard the idea that the market works in cycles, and that we are currently in the 4th such cycle. On the chart, I have pointed out the bull run portion of each of these 4 cycles.

Notice how the first bull run back in 2011 isn't even visible on the chart. The second one looks like an anthill. Even the 2017 run looks like a bunny hill compared to the current bull run, which absolutely towers over everything else.

This graph would appear to imply that the current bull run is by far the largest in history, and that they get smaller as you go back in time. This is true in terms of the absolute price (or equivalently market cap), but this can be deceiving. The reason it is deceiving is that absolute price change isn't what matters when it comes to investment growth. What matters for our investments is percentage change (or more technically: geometric change), not arithmetic price change. And in terms of percentage growth, the current bull run is by far the smallest of all the bull runs, and they get larger as you go back in time, generally speaking.

Before I go any further, let me be explicit about what linear space is: in linear space, a unit on the y-axis of a chart corresponds to some fixed quantity. On the chart in the image above, you ca

I don't want to step on anybody's toes here, but the amount of non-dad jokes here in this subreddit really annoys me. First of all, dad jokes CAN be NSFW, it clearly says so in the sub rules. Secondly, it doesn't automatically make it a dad joke if it's from a conversation between you and your child. Most importantly, the jokes that your CHILDREN tell YOU are not dad jokes. The point of a dad joke is that it's so cheesy only a dad who's trying to be funny would make such a joke. That's it. They are stupid plays on words, lame puns and so on. There has to be a clever pun or wordplay for it to be considered a dad joke.

Again, to all the fellow dads, I apologise if I'm sounding too harsh. But I just needed to get it off my chest.

Hey folks,

If you're like me, you've been feeling out the PvP super regen rates this past week and have been noticing some weirdness in how things seem to be working out. As it turns out, the new system for calculating super generation is rather complex and is the product of several intersecting systems.

In this post, I'm going to attempt to break down the numbers involved, what actions count for what, and how they work with standard play. It might get a bit wobbly in places, and, due to Bungie's new commitment to more regular and finer fine-tuning, the truth of these numbers could change later in the season. But, for now, even understanding the system itself will be an important part of discussions going forward.

Anyhow, let's jump in!

[Note: All numbers are an approximation to the closest possible measurable value. Rounding occurred after 2 decimal places. Some subjectivity within measurements is to be expected to due imperfect methods of capture]

Core Concepts to learn:

• Your subclass tier changes everything. It is the single most important thing to understand when trying to calculate super generation. This may sound obvious, but the details of why matter, so see below.
• Passive intellect gains matter, but not as much as you think.
• Killing enemies returns a flat amount of super energy. This return is less than what it was pre- Patch 3.4
• Weapon damage dealt with returns different amounts of super energy. This depends on if it's Primary, Special, or heavy.
• Damage taken returns the same super energy regardless of the weapon used to kill you.
• Ability damage does return super energy, however, the amount of damage needed is high and many abilities will return marginal super energy at best.
• Mods that return super energy (of those that work in PvP), can help but are no longer as efficient overall as before.

Super Energy and Super Units:

• Your Super Bar is a big ol' bucket that requires 460 somethings to fill it.
• For our purposes, let's call these somethings Super Units or SU for short.
• We generate SU in the following ways:
  • Passive Generation based on intellect
  • Active Generation is based on the intersection of Super Tier and what you are doing.

Passive Generation:

Just finished watching the big short for the first time. Holy fuck! This is going to be 2008 X420,690.

We're definitely getting a film like this and a netflix limited series post MOA$$. I reckon that's as close as the M🐍M will get to APES. MOA$$ is really going to fuck shit up. It was a small group that got insanely rich from that but there'll be a lot more this time. When none of them want to give interviews people are going to start to realise how untrustworthy the M🐍M really are. Anyone wants to interview me it better be an APE with a podcast, blog or own independent media outlet.

It's literally exactly the same shit all over again. Every thing happens for a reason and I'm glad I had to wait till now to watch that. I can't believe the same fucking people were brash enough to rob the world twice. Guy's that rob banks for a living are smarter than that. I've done a lot of dodgy shit in my life but when push came to shove shit hit the fan I had my day in court lost my cars, my flat, my business and my girlfriend I said I'm done with this I'm not doing it again. You know why? Because I was scared of the consequences.

What was it former president of United States the George W Bush said again? "Fool me once, shame on - shame on you. Fool me - you can't get fooled again". Need I say anymore!

I think this is the final nail in the coffin for centralised finance and it'll open the world's eyes to the many reasons central banks are not to be trusted. Just like they said in the new "future" South Park it was after the pandemic we realised that we are far better off trusting "fly by night crypto scams" than the likes of Kenny his hedge fund friends and media puppets.

It's one of the best decisions I ever made and it's the reason I'm here now. I got into stonks a year ago as a way to make a bit of extra legal tender and it's been one hell of a ride and we're only just sat down, buckled up and strapped in waiting for the most insane ride of our lives!

When these people got bailed out in 2008 they realised there are no negative consequences for their negative actions. So like any criminal with a lick of sense would, they started the operation up again but this time on crack and steroids. 2008 should have been the end but it was only the fucking start!

Crypto is tanking (harder than Kennys hair line), the POS brokerages have all shown their hands. As if that wasn't enough Evergrande is defaulting, the 1 year logarithmic charts got me jacked, jacked to th

So clearly the population units on planets cant be a 1 for 1 relationship. A system with 5 terraformed planets can't possibly have 43 people living in it.

So in my head, I started thinking that 1 pop unit = 1 billion people.

A terraformed planet can hold like 15 population, which would = 15 billion people.

This makes sense to me, because with better technology, there still would be a maximum number of people who could comfortably fit on one planet. After all we know they still need to grow food.

What do you think?

Anything I should know or practice. Gonna start by making an organized note sheet of the trig identities, logarithm rules, and unit circle.

Do your worst!

Recap of Part 1

FVC means "field-vectored craft," i.e., UFO(s).

We learned in Part 1:

• While landed on the ground, even smaller FVC are massive, i.e., have considerable mass around 30 tons (27,000 kgs).
• FVC are about as dense as a submarine and several times denser than aircraft, having around 96 percent the density of water.
• FVC are hard, solid, physical objects similar to metal.
• We have observed FVC at velocities of 5,000 to 9,000 mph (8,000 to 14,500 kph), with straight line and angular accelerations in the region of 100 times the acceleration of gravity. Although the accelerations are large for the size of the craft, human technology from the 1950s packaged electronics into smaller projectiles capable of withstanding 7,000 to 9,000 gs.
• The reason some craft appear as orbs of different colors is because the craft's propulsion system creates ionized and excited air molecules, namely a "plasma." Larger craft that use the most energy have a blue or ultraviolet plasma, while smaller craft that use less energy appear as red, orange, yellow, or green. The luminosity of a craft will increase as it puts out more power for high acceleration maneouvers. The plasma surrounding a craft often obscures an observer's ability to see the craft itself behind the plasma.
• The observed accelerations and velocities can be achieved with a high thrust-to-mass ratio. There is no need to presume FVC use exotic technology to reduce the mass of the craft while in flight. In general, all of the observables can be explained by established physics without resorting to speculative hypotheses. Finally, acceleration is not instantaneous but rather takes a non-zero amount of time, although the craft's swiftness may appear instantaneous to the naked eye.

Section IV: Radiation from FVC in the X-ray or Gamma Range

Date: January 30, 1973

Location: Lexington, Alabama

Witnesses: Bill Rogers, APRO Field investigator, and two other unnamed individuals.

Description: Rogers went to Lexington to investigate reports of FVC in the area, which began a month prior on December 27, 1972. Rogers, along with two other members of the investigation team, observed a yellowish-orange-white light moving slowly above tree-top level.

>After about a minute, the object moved up about 40 feet, and they could see that it had a shape between a sphere and an egg (ellipsoidal). It then descended

Video Link: A Guide to Loudness Perception

Since loudness is such an important topic in mixing it seems appropriate at this point to talk about the perception of loudness in general.

Loudness is measured in decibels (dB). Decibels are a relative, logarithmic measurement.

Decibels are a logarithmic measurement in that amplitude increases exponentially with decibel value. Specifically, every 10dB increase or decrease of decibel value corresponds to a factor of ten increase or decrease in amplitude. In other words, increasing a sound’s loudness by 10dB multiplies its amplitude by ten. Increasing a sound’s loudness by 20dB multiplies its amplitude by a hundred. Increasing a sound’s loudness by 30dB multiplies its amplitude by one thousandth. And so forth. Decibels are a relative measurement in that a measurement of decibels does not tell you precisely how loud a sound is; it can only tell you how loud it is relative to some reference amount, usually designated as 0dB. So, for instance, a level of 3dB is three decibels louder than the reference level, and a level of -3dB is three decibels quieter than the reference level.

When discussing real-world sounds traveling through the air, loudness is most often measured in dBSPL, or “decibels of sound pressure level.” This is a unit of measure based on the decibel, with the reference level of 0dBSPL being the quietest sound that is audible by a young adult with undamaged hearing. The threshold of pain is generally placed around 120dBSPL. This range of 0dBSPL to 120dBSPL gives us the practical dynamic range of human hearing. 80dBSPL is a good listening level for music.

Loudness can be measured in two ways: it can be measured in terms of peak loudness, or in terms of average loudness. Peak loudness measures the amplitude of the highest instantaneous peaks in the sound. Average loudness measures the overall average amplitude level, taking into account all of the loud peaks and the quiet in-between spaces. Peak loudness is good to know because peaks that are too loud will often cause audio equipment to overload. Average loudness is good to know because it reflects, more accurately than peak loudness, the human ear’s actual perception of loudness.

The level meters on most audio mixers measure peak loudness. Average loudness, when measured as described above, will still not be a terribly accurate measurement of human loudness perception. Loudness perception is complicated

For context I'm a Refuse Driver (Garbage man) & today I was on food waste. After I'd tipped I was checking the wagon for any defects when I spotted a lone pea balanced on the lifts.

I said "hey look, an escaPEA"

No one near me but it didn't half make me laugh for a good hour or so!

Edit: I can't believe how much this has blown up. Thank you everyone I've had a blast reading through the replies 😂

It really does, I swear!

Hi everyone, I’m a biomed doctor-wannabe who has recently completed the September 2021 GAMSAT and scored a 76 weighed (98th percentile) and 73 unweighed (65/67/86). I would like to share some experiences on how to do well on the gammie (especially on S3). At first glance, the gammie may look super scary, I mean, who isn’t intimidated by a 4.5 hr exam? However, you might be surprised at how minor changes in test-taking routines/strategies can make your life a million times easier.

On the day of the GAMSAT: Believe it or not, sitting the September GAMSAT during Melbourne lockdown 6.0 has certain advantages. For starters, S3 is sat on a different day to sections 1 and 2 (which are on the same day), ensuring that you are refreshed by the time you start it. However, you presumably won't have this luxury in March 2022, but you can still replicate it as much as possible. I sat a full length GAMSAT back in March 2021 and I can assure you that your brain will be fried by the time S3 begins. To remedy this, you must first stay hydrated (but you should also avoid going to the bathroom, my hack is to drink in little sips frequently as opposed to huge gulps at a time, you learn in physiology units that huge decreases in plasma osmolarity due to drinking lots of water will cause your body to break down circulating vasopressin, the hormone that prevents peeing). During the lunch break, eat a muesli bar which will both absorb the extra water that’s likely to steal a few minutes from you in a bathroom break and provide you with enough low-GI energy to power through S3 without a sugar crash. DO NOT under any circumstances eat a full meal during lunch break, you will feel drowsy right afterwards. If you want caffeine boosts, I found green tea to be a more sustainable source than coffee (no infamous coffee caffeine crash), but YMMV.

S1: My score was pretty average so I don’t have much to say about it. Please be aware that S1 requires fast reading skills and the ability to distinguish nuances between words. There's an element of luck to it because the options they give you for each question might be really nice or too similar to each other for you to distinguish. Although for certain questions they direct you to look at a specific line, you often need to view the preceding paragraphs in order for your answer to make sense in context (many distractor options would’ve been otherwise correct except they don’t suit the text’s context). You may think that S1 is reading comprehen

Just doing some pH analysis in chemistry and we are using this equation -log(M) in which M is in mols/liter. So what does taking the log of something do to units. What units would log (0.001 units) be?

They’re on standbi

Buenosdillas

RELEASE NOTES 1.20.6.0

To celebrate the launch of Windows 11, Microsoft Flight Simulator is lighting up some of the world’s most famous points of interest in Windows 11 colors! There is also a free livery for the EXTRA 330LT.

Stability

• Several crashes have been fixed across the title
• More optimization work has been performed including performance issue with Real-time AirTraffic after a long period of time
• Improvements of the installation logic for outdated / missing packages

Navigation

• New AIRAC cycle 2110 is now available
• Improvements on offset localizer/LDA approaches for the Navdata
• Updated the in-sim Magnetic Variation model
• Fixed ATC announcing a DME Arc approach with 10 times the radius
• Separated different airways with the same name in the Navdata
• Fixed cases of corruption in Title and Descr fields in flight plans

Weather

• Activated gust tweaking in custom weather settings
• Ambient pressure is now smoothly calculated across the entire air column
• Improved ATIS Cloud layer reporting

VR

• Fixed aliased menus and ingame panels
• Fixed some lighting issues in VR
• Fixed wrong camera initial rotation in some cockpit
• Fixed “dot” cursor when using the mouse
• Fixed mouse cursor depth when hovering the toolbar
• Improved general stability in VR mode

Activity

• Fixed Friends status as offline friends were still marked as online
• Better handling of edge cases when loading save files
• Fixed Balkan bushtrip which could not be completed due to missing airport
• Fixed conversion error in POH takeoff speeds in the Flight assistant panel
• Fixed issue where the altitude displayed on the nameplates was incorrect
• Fixed VFRMap icons disappearing during bushtrips
• Fixed bug causing the female voice to be heard instead of MALE voice in the Deadstick Landing tutorial
• Fixed ICAOs on main path disappearing from the VFR map after resizing it

Planes

General:

• Fixed a bug that prevented Live/AI aircrafts lights from showing
• Reduced the effect of clouds water density on air density (source of drag when flying through clouds) by a factor of 10x
• Altimeter reading should now properly coincide mathematically with atmosphere ambient pressure
• Fixed physical altimeters so they can now display different values
• Fixed UseTemplateValue put inside an Action for custom checklists
• Corrected issue that would cause trim keys to start repeating instantly when held down
• Fixed shar

Pilot on me!!

The question asks to first find the inverse of y = 4 + 2 log₂(x), which is y = 2***^(x/2 - 2)***:

x - 4 = 2 log₂(y)
x/2 - 2 = log₂(y)
y = 2^(x/2 - 2)

Then, it asks to find the intersections between these two. I know that the intersections between a function and its inverse lie on y = x, so I now have three equations to work from:

1. 4 + 2 log₂(x) = x
2. 2^(x/2 - 2) = x
3. 4 + 2 log₂(x) = 2x^(/2 - 2)

I've tried manipulating both in Desmos - because this sub doesn't allow images for some reason, I'll attempt to typeset my attempts for Rule 2.

Attempt 1:

4 + 2 log₂(x) = x
log₂(16) + log₂(x**^(2)) = x * log₂(2)
log₂(16x^(2)) = log₂(2^(x)**)
16x^(2) = 2^(x)

Attempt 2:

2^(x/2 - 2) = x
log₂(x) = x/2 - 2
log₂(x) + 2 = x/2
2 log₂(x) + 4 = x
log₂(x**^(2)) + log₂(16) = x
log₂(16x^(2)**) = x
16x^(2) = 2^(x)

Attempt 3:

4 + 2 log₂(x) = 2^(x/2 - 2)
2 log₂(x) = 2^(x/2 - 2) - 2^(2)
log₂(x) = 2**^(x/2)/8 - 2
2 + log₂(x) = 2^(x/2)/8
log₂(4) + log₂(x) = 2^(x/2)/8
log₂(4x) = 2^(x/2)/8
8 log₂(4x) = 2^(x/2)
log₂(65536x^(8)) = 2^(x/2)
(log₂(65536x^(8)**))^(2) = 2^(x)

From the last two attempts:

(log₂(65536x**^(8)))^(2) = 16x^(2) = 2^(x)
(log₂(65536x^(8)))^(2) = 16x^(2)
log₂(65536x^(8)) = 4x
x = 1/4 * log₂(65536x^(8))
x = log₂(16x^(2)**)
16x^(2) = 2^(x)

I keep coming to the same equation that I can't seem to simplify. I see that both sides have 2 as a common factor, but turning 16 into 2^(4) just makes the RHS 2^(x - 4). Any and all help is appreciated! :)

I'm surprised it hasn't decade.

Just finished watching the big short for the first time. Holy fuck! This is going to be 2008 X420,690.

We're definitely getting a film like this and a netflix limited series post MOA$$. I reckon that's as close as the M🐍M will get to APES. MOA$$ is really going to fuck shit up. It was a small group that got insanely rich from that but there'll be a lot more this time. When none of them want to give interviews people are going to start to realise how untrustworthy the M🐍M really are. Anyone wants to interview me it better be an APE with a podcast, blog or own independent media outlet.

It's literally exactly the same shit all over again. Every thing happens for a reason and I'm glad I had to wait till now to watch that. I can't believe the same fucking people were brash enough to rob the world twice. Guy's that rob banks for a living are smarter than that. I've done a lot of dodgy shit in my life but when push came to shove shit hit the fan I had my day in court lost my cars, my flat, my business and my girlfriend I said I'm done with this I'm not doing it again. You know why? Because I was scared of the consequences.

What was it former president of United States the George W Bush said again? "Fool me once, shame on - shame on you. Fool me - you can't get fooled again". Need I say anymore!

I think this is the final nail in the coffin for centralised finance and it'll open the world's eyes to the many reasons central banks are not to be trusted. Just like they said in the new "future" South Park it was after the pandemic we realised that we are far better off trusting "fly by night crypto scams" than the likes of Kenny his hedge fund friends and media puppets.

It's one of the best decisions I ever made and it's the reason I'm here now. I got into stonks a year ago as a way to make a bit of extra legal tender and it's been one hell of a ride and we're only just sat down, buckled up and strapped in waiting for the most insane ride of our lives!

When these people got bailed out in 2008 they realised there are no negative consequences for their negative actions. So like any criminal with a lick of sense would, they started the operation up again but this time on crack and steroids. 2008 should have been the end but it was only the fucking start!

Crypto is tanking (harder than Kennys hair line), the POS brokerages have all shown their hands. As if that wasn't enough Evergrande is defaulting, the 1 year logarithmic charts got me jacked, jacked to th