JAMB 1992 · UME · Q4✱✱

What is the value of $x$ satisfying the equation $\frac{4^{2x}}{4^{3x}} = 2$ ?

Worked solution (try it first)

Dividing powers of the same base, subtract the indices: $4^{2x - 3x} = 4^{-x}$ , so $4^{-x} = 2$ .
Write 4 as $2^2$ : $2^{-2x} = 2^1$ .
Equate the powers: $-2x = 1$ , so $x = -\frac12$ , option B.