2^x - 2^x-2 = 3(2^13)
=> 2^(x-2+2) - 2^x-2 = 3(2^13) (x can be written as x-2+2)
=> (2^x-2).(2^2) - 2^x-2 = 3(2^13)
=> 2^x-2(2^2-1) = 3(2^13)
=> 2^x-2(3) = 3(2^13) => x - 2 = 13 => x = 15

Hope it helps :)