JAMB 1993 · UME · Q3

If $9^{x - \frac12} = 3^{x^2}$ , find the value of $x$ .

Worked solution (try it first)

Write 9 as $3^2$ and multiply the indices: $9^{x - \frac12} = 3^{2x - 1}$ .
The bases match, so the powers are equal: $2x - 1 = x^2$ , or $x^2 - 2x + 1 = 0$ .
This is $(x - 1)^2 = 0$ , so $x = 1$ , option B.