Log, ln, e, and other math

[thenykway]

Hey guys, my test is in 2 days and I'm just about wrapping up reviewing everything.

I noticed in the Berkeley books (my main study source), theres a lot of math involved where as in on the AAMC tests, all the math is basic algebra on a 10th grade level.

However, there are some concepts like log, ln, e that I'm kind of iffy on/paranoid that itll show up a lot. What exactly do I need to know about them on the MCAT level?

So far what I know about "log" (please correct me if I'm wrong):

log 10^x = x
log 1= 0
log 2 = .30
log 3 = .48
log of a fraction = a negative number (right?)

and when trying find, lets say log 8. log 8 = log 2x2x2 = log 2 + log 2 + log 2 = ;30 +.30 +.30 = .90


and I know absolutely nothing about ln and e... all I know is that they have to do with natural log... can someone fill me in on these? (only if we REALLY need to know a lot about it... i could be using my limited time on better things haha)

Are there any other more "complicated" math concepts I should know for this test?

Thanks!

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[Jepstein30]

Hey guys, my test is in 2 days and I'm just about wrapping up reviewing everything.

I noticed in the Berkeley books (my main study source), theres a lot of math involved where as in on the AAMC tests, all the math is basic algebra on a 10th grade level.

However, there are some concepts like log, ln, e that I'm kind of iffy on/paranoid that itll show up a lot. What exactly do I need to know about them on the MCAT level?

So far what I know about "log" (please correct me if I'm wrong):

log 10^x = x
log 1= 0
log 2 = .30
log 3 = .48
log of a fraction = a negative number (right?)

and when trying find, lets say log 8. log 8 = log 2x2x2 = log 2 + log 2 + log 2 = ;30 +.30 +.30 = .90


and I know absolutely nothing about ln and e... all I know is that they have to do with natural log... can someone fill me in on these? (only if we REALLY need to know a lot about it... i could be using my limited time on better things haha)

Are there any other more "complicated" math concepts I should know for this test?

Thanks!

You should know log 2 and log 3 and how to work with them to estimate other logs. Most likely, you won't have to use that info on the MCAT but its quick enough to learn that its worthwhile. As for ln and e, that's just log using a different base. I doubt you'd have to know anything about that other than how to manipulate algebraically.

best to work in scientific notation for logs

ex. log of 2*10^-4 = -4+.3= -3.7

exponent = what comes out of log, keep the negative
add terms together since its multiplication

if we have something more complicated like:

log of 5*10^5 = 5 + (log 10/2) = 5+ log 10/log 2 = 5 + 1 - .3

convert into easy terms to work with (2, 3 and 10).
subtraction of terms because its division

 

[reising1]

I'm taking it in 2 days too!! Good luck to you!

You'll definitely want to know quickly for pH stuff that -log(10^-X) = X

You'll also want to know quickly for pH stuff that -log(Y * 10^-X) is less than X if Y is greater than 1. This is especially important when they give you a difficult molarity or if it's a dilute acid, you need to consider the H+ molarity of water. For example, a 10^-8 M solution of HCl does not have a pH of 8, but rather, a pH of 10^-8 + 10^-7 which is 1.1 * 10^-7, and -log(1.1*10^-7) is about 6.96

I wouldn't worry about knowing anything about ln(x), but maybe what the plot looks like.

The only use for knowing "e" is for Arhenius equation K = Ae^(-Ea/RT). For this, it's useful to know how changing Ea and T affects K. Rather than memorizing this, I tend to like to rewrite the formula. We know that "e" is just a constant. Just as 10^-3 is the same as 1/(10^3), we can rewrite the Arrhenius equation to be K = A/(e^Ea/RT). And if you remember that "e" is just a number, you can make easier predictions about the values. For example, in this form, if you increase T, then it's e^(smaller number) on the bottom of the fraction, which means it is A/(smaller number) which means that K is increased.