Can you explain how to solve 4^X · (½)^3-2X=8 · (2^X)^2 and 4^X-3=8^4-X?

Answer 1

4^X · (½)^3-2X=8 · (2^X)^2
2^(2x(1/8-2x)) = 2^3(2^(2x)) = 2^(2x+3)
2x(1/8-2x)= 2x+3
x/4-4x^2 =2x+3
4x^2 + 7x/4 +3 = 0
Use quadratic formula to solve

4^(X-3)=8^(4-X)
2^(2x -3) = 2^(12-3x)
2x-3 = 12-3x
5x = 15
x = 3