algebric equation

[hetavdave]

I was able to guess the correct answer but can anyone please explain the answer in detail.

If 2^x - 2^x-2 = 3(2^13) then what is value of x?

a. 9
b. 11
c. 13
d. 15
e. 17

OA
d

[DanaJ]

It's only a matter of seeing the common factor of 2^x and 2^(x-2). It will be 2^(x-2):

2^x - 2^(x-2) = 2^(x-2)*(2^2 - 1) = 2^(x-2)*3

Since you have 2^(x - 2)*3 = 3*2^13, you get that x - 2 = 13, with x = 15.