JAMB 2003 · UME · Q11

If $\dfrac{9^{2x - 1}}{27^{x + 1}} = 1$ , find the value of $x$ .

Worked solution (try it first)

Write both as powers of 3: $9^{2x - 1} = 3^{4x - 2}$ and $27^{x + 1} = 3^{3x + 3}$ .
A fraction equal to 1 has top equal to bottom, so $4x - 2 = 3x + 3$ .
Solve: $x = 5$ , option C.