show that 5*2^x-2^x-2=2^x

Question

it's a show that question and I'm in 11th grade

Answer 1

First, let's put x=0 in the proposed equality, then 2^x=2⁰=1:

5×1-1-2=1 is not true so the equality is false. The proposed equality is not true.

5×2^x-2^x-2=4×2^x-2=2²×2^x-2=2^x+2-2=2(2^x+1-1). So the RHS=2, 6, 14, 30, as x=0, 1, 2, 3.

There is an error in the question or the question has been wrongly expressed.

(5×2^x-2^x)/2²=2^x, for example, is true.