JAMB 2012 · UTME · Q6

If $27^{x + 2} \div 9^{x + 1} = 3^{2x}$ , find $x$ .

Worked solution (try it first)

Write both as powers of 3: $27^{x + 2} = 3^{3x + 6}$ and $9^{x + 1} = 3^{2x + 2}$ .
Dividing, subtract the indices: $3^{(3x + 6) - (2x + 2)} = 3^{x + 4}$ .
So $x + 4 = 2x$ , which gives $x = 4$ , option B.