Before I returned to college, I intended to become a mathematician, and spent a year teaching myself advanced calculus, topology, abstract algebra, and the like. Unfortunately, before I took the DAT I hadn't had a math class in over four years, and all I did to study was do 155 Destroyer problems, and only managed a 21.
I would recommend memorizing the following:
10^n, where n = 0.5, 1.5, 2.5, 3.5,...
= 3.16 x 10^(n - 0.5)
10^n, where n = 0.25, 1.25, 2.25, 3.25,...
= 1.78 x 10^(n - 0.25)
10^n, where n = 0.75, 1.75, 2.75, 3.75,...
= 5.62 x 10^(n - 0.75)
Now when you're working with negative numbers, the trend stays the same for -0.5, but simply reverses for -0.25 and -0.75. So we have the following:
10^n, where n = -0.5, -1.5, -2.5, -3.5,...
= 3.16 x 10^(n - 0.5)
10^n, where n = -0.25, -1.25, -2.25,..
= 5.62 x 10^(n - 0.75)
10^n, where n = -0.75, -1.75, -2.75,...
1.78 x 10^(n - 0.25)
How will this help you on the DAT?
Well let's say you get a question that requires you to solve log(375) = n
So how do we get n? Well, let's re-write it as log(3.75 x 10^2) = n
Then we get log(3.75) + log(10^2) = n
Well, we know what log(10^2); that's just 2. But what's log(3.75)?
Well it would be 10^n = 3.75. We know that it would be higher than 0.5, because 10^0.5 = 3.16, but less than 0.75, because 10^0.75 = 5.62.
So our answer would be 2 + 0.6, or 2.6.
And indeed, log(375) = 2.57!
With practice, you can do these sort of calculations very rapidly. Feel free to write back if you need more help!
