JAMB 1997 · UME · Q5

Simplify $\log_2 96 - 2\log_2 6$ .

Worked solution (try it first)

Move the 2 up as a power: $2\log_2 6 = \log_2 36$ , so the expression is $\log_2 \frac{96}{36} = \log_2 \frac83$ .
Split the fraction: $\log_2 \frac83 = \log_2 8 - \log_2 3$ .
$\log_2 8 = 3$ , so the answer is $3 - \log_2 3$ , option B.