Solve for X as an exponent

[jamesdougnelson]

2^x - 2^(x-2) = 3(2^13), solve for x.

This one has really got me stumped. Any help out there?

[gmatmachoman]

2^x - 2^(x-2) = 3(2^13), solve for x.

This one has really got me stumped. Any help out there?

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

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

2^X = 2 ^15

equating the powers of 2, we have X = 15..

[Rahul@gurome]

Solution:
2^x - 2^(x-2) = 2^x - 2^x * 2^(-2)
= 2^x - 2^x/(2^2) = 2^x - 2^x/4 = 2^x(1-1/4)
= 2^x*3/4
So 2^x * ¾ = 3 * 2^13 implies 2^x = 2^13*4 = 2^13*2^2 = 2^15.
Or x = 15.