When you have that, factorize the same ones.

2^x - 2^x-2=3(2^13)
2^(x-2).(2^2-1)=3(2^13)
3.2^(x-2)=3(2^13)
2^(x-2)=(2^13)
x-2=13
x=15

You have to factorize and know that 2^x=2^(x-2) . 2^2

( the "." mean multiply)

dint get it

i wud like to add just one step which might help remove ur confusion...

2^x - 2^x-2=3(2^13)

(2^x)-(2^x)(2^-2)=3(2^13)

If 2^x - 2^x-2=3(2^13), what is the value of x

just understand one simple thing

2^x-2 can be written as 2^x/2^2 = 2^x/4 ( a^m/a^n= a^m-n)

thats it

take 2^x common in the equation

2^x( 1- 1/4) = 3(2^13)

solve this

2^x (3/4) = 3(2^13)

cancel 3 on both sides

2^x = 4( 2^13)

2^x = 2^2* 2^13 ( a^m*a^n = a^m+n)

there fore x =15

i hope it helps ...