WAEC 2021 · Paper 1 · Q4

If $\log_{10} 2 = m$ and $\log_{10} 3 = n$ , find $\log_{10} 24$ in terms of $m$ and $n$ .

Worked solution (try it first)

Write 24 using 2 and 3: $24 = 8 \times 3 = 2^3 \times 3$ .
The log of a product is the sum of the logs, and a power comes down in front: $\log 24 = 3\log 2 + \log 3$ .
So $\log 24 = 3m + n$ , option A.