Question

2^2x - 2^x+3 + 2^4 = 0 how to prove this?

Answer 1

22x+3(2x)−4=022x+3(2x)−4=0

(2x)2+3(2x)−4=0(2x)2+3(2x)−4=0

Let u=2xu=2x

u2+3u−4=0u2+3u−4=0

(u−1)(u+4)=0(u−1)(u+4)=0

u=1u=1or u=−4u=−4

2x=12x=1 or 2x=−42x=−4

Since 2x2x can never be negative, we only need to solve 2x=12x=1 which can easily be solved to find x=0x=0 as the only real solution to the original equation