How do I solve this equation?

Question

4^x * (1/2)^3-2x = 8*(2^x)^2

Answer 1

I assume you meant (1/2)^(3-2x). If so, make everything powers of 2 and you have

2^(2x) * 2^(2x-3) = 2^3 * 2^(2x)
so, adding powers,
2x + 2x-3 = 3 + 2x
x=3