SunnyD0119 said:
See on kaplan subject tests they want you to solve for x using like 3rd root 4.5 x10^-8 all over 4 i dont know how to do that crap in my head?
are there calcs like this on the real deal?
Usually such calculations are used for calculating the concentration of H+ and eventually the pH. This involves taking -log of x. To solve this quickly in your head don't simplify the 3rd root 4.5 x10^-8 all over 4. Write this as x=(4.5x10^-8 / 4)^(1/3)
Then, pH = - log (4.5x10^-8 / 4)^(1/3)
which implies pH = - (1/3) log (4.5x10^-8 / 4)
Just roughly divide the 4.5 with 4 (leaving the 10 ^-8 out) in your head and the answer you'll get will be a little more than 1. Do it on paper and you'll get 1.1
Now brin back the 10^-8
Therefore, the answer to 4.5x10^-8 / 4 = 1.1 x10^-8
the whole expression now looks like: - (1/3) log 1.1 x10^-8
Now you have to take the - log 1.1 x10^-8 which is equal to = 8 - log 1.1
Since the log of 1 is 0, the log of 1.1 can be assumed to be equal to 0 also.
Now the whole expression has simplified to pH = (1/3) x 8 = 8/3
This can easily be divided on paper and the answer would be 2.66.
Search for the answer closest to 2.66 in the answer choices.
I agree... without the log involved this would be difficult to do it in head.
but then again... you can always use graph theory for estimating this
😉 (courtesy of math minor).