JAMB 1990 · UME · Q10

Simplify $3\log_6 9 + \log_6 12 + \log_6 64 - \log_6 72$ .

Worked solution (try it first)

Move the 3 up as a power: $3\log_6 9 = \log_6 9^3 = \log_6 729$ .
Adding logs multiplies and subtracting divides, so the expression is $\log_6 \frac{729 \times 12 \times 64}{72}$ .
$\frac{12}{72} = \frac16$ , so the number inside is $\frac{729 \times 64}{6} = 7776$ , which is $6^5$ .
So the value is $\log_6 6^5 = 5$ , option A.