WAEC 2023 · Paper 1 · Q18

Simplify: $\dfrac{\log\sqrt{27} - \log\sqrt{8}}{\log 3 - \log 2}$ .

Worked solution (try it first)

Write the roots as powers: $\sqrt{27} = 3^{3/2}$ and $\sqrt{8} = 2^{3/2}$ .
Bring the powers down: the top is $\frac{3}{2}\log 3 - \frac{3}{2}\log 2 = \frac{3}{2}(\log 3 - \log 2)$ .
Cancel $(\log 3 - \log 2)$ with the bottom to leave $\frac{3}{2}$ , option D.