how to solve logs mcat

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By submitting my email address. i certify that i am 13 years of age or older, agree to recieve marketing email messages from the princeton review, and agree to terms of use., how to survive mcat math without a calculator.

The MCAT is essentially a science test, but you’ll still need a solid grasp of math fundamentals to score big —and you cannot use a calculator.

Our experts compiled a list of MCAT math topics to prep for along with some tips for doing math calculations by hand.

What math is covered on the MCAT?

The MCAT is primarily a conceptual exam, with little actual mathematical computation. Any math that is on the MCAT is fundamental: just arithmetic, algebra, and trigonometry. There is absolutely no calculus on the MCAT. Math-based problems will appear mostly in the Chemical and Physical Foundations of Biological Systems section . On the other science sections, a basic understanding of statistics as used in research will be helpful.

MCAT Math Tricks

1. practice for not having a calculator..

You aren’t allowed to use a calculator on the MCAT, so you need to practice doing arithmetic calculations by hand. Fortunately, the amount of calculation you’ll have to do is small. See how you score on our free MCAT practice test .

2. You only have to be reasonably accurate.

Try to make approximations so that you can do the math quickly. On the Chem/Phys section, your MCAT time per question is approximately 1.4 minutes (95 minutes for 67 questions). There simply isn't time for lengthy, complicated math!

Here's how it works. Which of the following calculations for figuring out the value of 23.6 × 72.5 is faster?

In the one-step calculation on the right, we approximated: 23.6 ≈ 25 and 72.5 ≈ 70. The answer we got in just a few seconds differs from the precise answer by only 2%. For the MCAT, you should always try to approximate so that you can do the math quickly.

Free MCAT Practice Tests & Events

Evaluate and improve your MCAT score.

3. Remember to pace yourself

If you find yourself writing out convoluted calculations on your scratch paper when you’re working through math-based MCAT problems, it’s important that you recognize that you’re not using your time efficiently. Say to yourself, “I’m wasting valuable time trying to get a precise answer, when I don’t need to be precise.”

4. Include some math review in your MCAT prep 

Are you rusty in any of these areas? You'll want to brush up on a few key math concepts during your MCAT prep .

Arithmetic, Algebra, Graphs

• Scientific notation, exponents, and radicals
• Fractions, ratios, and percents
• Equations and inequalities
• x-y  plane, lines, and other graphs

Trigonometry

• Pythagorean Theorem
• Sine, cosine, and tangent functions
• Sine and cosine values of common angles
• Inverse functions
• Radian measure
• Scalars and vectors
• Addition and subtraction of vectors
• Scalar multiplication
• Vector projections and components

Proportions

• Direct proportions
• Inverse proportions
• Laws of logarithms

Basic Statistics

• Mean, median, mode, range
• Standard deviation, normal distributions
• Variables, sample size, random samples, correlation
• Reliability, validity
• Randomized controlled trial, double-blind experiment

Research Methods

• Graphical analysis and interpretation
• Determining whether results are supported by data presented in figures
• Demonstrating an understanding of basic statistics and research methods
• Interpreting data presented in graphs, figures, and tables
• Drawing conclusions about data and methodology

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Video Transcript: MCAT Antilogs Without A Calculator

June 9, 2014 By Leah4sci 1 Comment

( click here to watch on YouTube )

[Start Transcript]

Leah here from Leah4sci.com/MCAT and in this video, I’ll show you how to solve MCAT style Antilogs questions without a calculator.  This video picks up from my last video where I show you how to solve logarithm based questions and you can find this video alongwith my entire series on solving MCAT Math without a calculator by visiting my website https://leah4sci.com/MCATMATH.

In the last video I showed you a trick on how to find a pH, pOH or pKa  value when given a concentration or ka. The trick showed you that when you have a number times ten to a negative power, that power becomes your pka, your pH or your poH.

But what if now you are faced with a question where the actual pH, poH or pka value is given and you’re ask to find the concentration or the ka? For  example you maybe given a question that says:

Find the ka of an acid whose buffer has a pH of 4.19 in a solution containing equal moles of acid and conjugate base.

I’ll cover the Science portion of this question in my Chemistry videos at leah4sci.com/MCATCHEMISTRY but for this video let focus just on the Math. Since we’re dealing with a buffer we’ll use the Henderson–Hasselbalch equation which says that pH is equal to pka plus the log of Conjugate base over acid.

You’ll also see this written as A minus over HA. Even though we have equal moles of acid and conjugate base or fifty-fifty, whatever number we have for conjugate base is the number for acid and that means we have a ratio of some number over itself or one.

The log of one is zero and that means this entire portion of the equation drops out telling me that the pH is equal to the pka. Knowing that the pH is equal to 4.19 equals the pka we know the pka is also equals to 4.19. But how do we use this to find the ka value of this acid? 4.19 is not a clean and easy number to calculate so let’s break it down:

The first thing you want to do is check how close your answer choices are to each other to see how much you can simplify and how quickly you can come up with the answer. Here’s the equation we’ll use. If pka is equal to negative log of ka (pka= -log ka), since log stands for log base ten, to solve for ka we have to have ten to the power of negative log to cancel out and that means we need ten to the power of negative pka. So the ka value is equal to ten to the minus pka which is equal to ten to the minus four point one nine (ka = 10^pka = 10^-4.19).

A nice and clean number like four would give us a ka value of one times ten to the minus four. But we also have to account for that 4.19 so we don’t know we’re looking for the number close to one times ten to the minus four. If this is not enough to isolate your answer, you then want to find the range where your ka will fall out.

We’ll take the number 4.19 and round it down to 4 and up to 5. A pka of  4 has a ka of one times ten to the minus four, a pka of 5 has a ka of one times ten to the minus five. That means the number we’re looking for is somewhere in this range. But if this is still not enough, then you wanna go back to the trick where I showed you how to recognize the different numbers that give you different ranges. In review, if we have a number point one we get an eight time ten to the minus x. And I put  x instead of the number because if we have 4.19 our exponent will be a number times ten to the minus five.  So if we had 4.1 it will be eight times ten to the minus five.

A number point three will be five times ten to the minus that power. In this case, if we have 4.19, let’s round that to 4.2, remember on the MCAT you are allowed to round because it will be close enough. If point one gives me an eight and point five gives me a five then our answer has to be somewhere between eight and five so all you have to recognize is that the number is somewhere between five and eight. So it’ll be five times ten to the minus five to eight times ten to the minus five.

Even if we haven’t narrowed in on a specific number, for the MCAT this is close enough. In fact, punching ten to the negative four point one nine in the calculator I get an answer of 6.46 times ten to the minus five which on the MCAT is close enough. If you wanna narrow this down a little more, 4.19 is closer to 4.1 than it is to 4.3 and that means we’ll be closer to the 8 than to the 5 as is evident by 6.46.

This concludes my video series on MCAT Math Without a Calculator. You can find this entire series on my website at https://leah4sci.com/MCATMath . You can find additional MCAT videos including Physics, Chemistry, Biology and Organic Chemistry on my website https://leah4sci.com/MCAT

Are you stuck on a specific MCAT topic? I offer Private Online Tutoring where I focus on your needs to strengthen your individual weaknesses. Tutoring details can be found using the link below or by visiting my website leah4sci.com/MCATTutor.

Are you overwhelmed by the sheer volume of information required for the MCAT? Are you worried that lack of a proper study plan and low MCAT score will prevent you from getting into Medical School?

My new ebook The MCAT Exam Strategy is 6-Week Guide to Crushing the MCAT will help you formulate a concrete study plan by helping you figure out where you stand now, identify your goals and figure out what it takes to reach them and it’s yours FREE when you sign up for my email newsletter at MCATExamStrategy.com.

By signing up for my email newsletter, you’ll also be the first to know when I have new videos, MCAT Study Guide Cheat Sheets Tips and so much more! The link again  MCATExamStrategy.com.

[End Transcript]

Watch the Video Here:  MCAT Math Video 9 – Antilogs

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• Main content

Everyone's talking about OpenAI's Q*. Here's what you need to know about the mysterious project.

• A mysterious new OpenAI model known as Q* has got the tech world talking.
• The model is said to have sparked concern at the startup that led to the resulting chaos.
• AI experts say the model could be a big step forward but is unlikely to end the world anytime soon.

As the dust settles on the chaos at OpenAI, we still don't know why CEO Sam Altman was fired — but reports have suggested it could be linked to a mysterious AI model .

The Information reported that a team led by OpenAI chief scientist Ilya Sutskever had made a breakthrough earlier this year, which allowed them to build a new model known as Q* (pronounced "Q star.") The outlet reported that the model could solve basic math problems.

Sources told Reuters that this model provoked an internal firestorm , with several staff members writing a letter to OpenAI's board warning that the new breakthrough could threaten humanity.

This warning was cited as one of the reasons that the board chose to fire Sam Altman, who returned as CEO on Wednesday after days of turmoil at the company, Reuters reported.

The ability to solve basic math problems may not sound that impressive, but AI experts told Business Insider it would represent a huge leap forward from existing models, which struggle to generalize outside the data they are trained on.

"If it has the ability to logically reason and reason about abstract concepts, which right now is what it really struggles with, that's a pretty tremendous leap," said Charles Higgins, a cofounder of the AI-training startup Tromero who's also a Ph.D. candidate in AI safety.

He added, "Maths is about symbolically reasoning — saying, for example, 'If X is bigger than Y and Y is bigger than Z, then X is bigger than Z.' Language models traditionally really struggle at that because they don't logically reason, they just have what are effectively intuitions."

Sophia Kalanovska, a fellow Tromero cofounder and Ph.D. candidate, told BI that Q*'s name implied it was a combination of two well-known AI techniques, Q-learning and A* search.

She said this suggested the new model could combine the deep-learning techniques that power ChatGPT with rules programmed by humans. It's an approach that could help fix the chatbot's hallucination problem .

"I think it's symbolically very important. On a practical level, I don't think it's going to end the world," Kalanovska said.

"I think the reason why people believe that Q* is going to lead to AGI is because, from what we've heard so far, it seems like it will combine the two sides of the brain and be capable of knowing some things out of experience, while still being able to reason about facts," she added, referring to artificial general intelligence.

"That is definitely a step closer to what we consider intelligence, and it is possible that it leads to the model being able to have new ideas, which is not the case with ChatGPT."

The inability to reason and develop new ideas, rather than just regurgitating information from within their training data, is seen as a huge limitation of existing models, even by the people building them .

Andrew Rogoyski, a director at the Surrey Institute for People-Centered AI, told BI that solving unseen problems was a key step toward creating AGI.

"In the case of math, we know existing AIs have been shown to be capable of undergraduate-level math but to struggle with anything more advanced," he said.

"However, if an AI can solve new, unseen problems, not just regurgitate or reshape existing knowledge, then this would be a big deal, even if the math is relatively simple," he added.

Not everyone was so enthused by the reported breakthrough. Gary Marcus, an AI expert and deep-learning critic , expressed doubts about Q*'s reported capabilities in a post on his Substack .

"If I had a nickel for every extrapolation like that—'today , it works for grade school students! next year, it will take over the world!'—I'd be Musk-level rich," wrote Marcus.

OpenAI did not immediately respond to a request for comment from Business Insider, made outside normal working hours.

Watch: Sam Altman moves to Microsoft after OpenAI fires him as CEO