1 question per post per customer! Also, in future, please post in the problem solving or data sufficiency sub forum, as appropriate. Hey, please include the source and the answer choices as well!
(If you do a search on your second question, you'll see that it's been answered many times.)
if 2^x - 2^(x-2) = 3(2^13), what is x?
Let's start by focusing on the left side of the equation:
2^x - 2^(x-2)
There's no simple way to add or subtract exponents unless they have the same power AND the same base. So, we need to rewrite this expression so the power and base are equal. We do so by factoring down to the smaller power.
2^x - 2^(x-2)
We can rewrite 2^x as:
(2^2)(2^(x-2))
4(2^(x-2))
We can rewrite 2^(x-2) as:
1(2^(x-2))
So, we have:
4(2^(x-2)) - 1(2^(x-2)) = 3(2^(x-2))
Plugging that back into the original equation, we get:
3(2^(x-2)) = 3(2^13)
so, we know that:
x - 2 = 13
x = 15
