JAMB 1989 · UME · Q11

Find $p$ in terms of $q$ if $\log_3 p + 3\log_3 q = 3$ .

Worked solution (try it first)

Move the 3 up as a power: $3\log_3 q = \log_3 q^3$ , so the left side is $\log_3 (pq^3) = 3$ .
Change to index form: $pq^3 = 3^3 = 27$ .
So $p = \frac{27}{q^3}$
$= \left(\frac3q\right)^3$ , option A.