WAEC 2019 · Paper 1 · Q14

Simplify $\log_{10} 6 - 3\log_{10} 3 + \frac23\log_{10} 27$ .

Worked solution (try it first)

Move the numbers up as powers: $3\log 3 = \log 27$ , and $\frac23\log 27 = \log 27^{\frac23}$
$= \log 9$ .
Combine: $\log 6 - \log 27 + \log 9 = \log \frac{6 \times 9}{27}$ .
$\frac{54}{27} = 2$ , so the answer is $\log_{10} 2$ , option B.