tncekm's math is dead on. And he's mostly correct in saying that you'll never really need to get the exact number for pH. BUT, the MCAT can test you on pHs down to about ~.5 a pH! So you need to know how to differentiate whether something is above or below of pH of say 2.5. (or 3.5 or 4.5 etc...)
Let me help you out with a neat little estimation trick.
So we know that:
[H+] of 1x10^-4 = pH 4
and
[H+] of 1x10^-3 = pH 3
But what if the MCAT asks you to differentiate between two answer choices that are something like:
a) pH of 3.15
b) pH of 3.55
So how do you deal with those 'middle' pHs? Well in the above example, remember that a multiplier of '3' in front of the x10^-4 in the H+ concentration puts you right in between two integer values of pH. Example:
Since,
[H+] of 1x10^-4 = pH 4
and,
[H+] of 1x10^-3 = pH 3
Then,
[H+] of
3x10^-4 is ~ pH 3.5
So if the multiplier is above or below '3', you can estimate whether the answer is above or below pH 3.5.
In your problem you have an [H+] of 7x10^-4, then since 7 is greater than 3, it means that the pH is LOWER than 3.5 but greater than 3! (Remember that higher H+ means lower pH.)
See how you could have done that problem in literally 2 seconds if you get comfortable with the rounding trick? You would never have to break up the log into parts and then do all that hairy math. 2 seconds is all it takes, and no paper work!
So just remember that:
[H+] of 3x10^-10 will be pH 9.5
[H+] of 3x10^-9 will be pH 8.5
[H+] of 3x10^-8 will be pH 7.5
etc...
And then if you get a weird [H+] like 8.342x10^-7, you know immediately that since 8.342 is greater than 3, the pH is going to be less than 6.5 but greater than 6...in this case since 8.342x10^-7 is closer to 1x10^-6, the pH is going to be very near to 6. (It's actually 6.078)
This little trick is sufficient for estimating these problems on the MCAT and cut your calculations down to zero! It'll save you a lot of time on these types of problems.
Did you guys understand that?
