JAMB 1989 · UME · Q17

Find the positive number $x$ such that $2^{x^3 - x^2 - 2x} = 1$ .

Worked solution (try it first)

$2^0 = 1$ , and no other power of 2 equals 1, so the index must be 0: $x^3 - x^2 - 2x = 0$ .
Factorise: $x(x^2 - x - 2) = x(x - 2)(x + 1) = 0$ , so $x = 0$ , 2 or $-1$ .
The only positive one is $x = 2$ , option C.