JAMB 2000 · UME · Q11

Evaluate $5^{-3\log_5 2} \times 2^{2\log_2 3}$ .

Worked solution (try it first)

Move the $-3$ inside: $-3\log_5 2 = \log_5 2^{-3}$
$= \log_5 \frac18$ .
Since $a^{\log_a N} = N$ , the first factor is $\frac18$ .
In the same way $2\log_2 3 = \log_2 9$ , so the second factor is $2^{\log_2 9} = 9$ .
So the value is $\frac18 \times 9 = \frac98 = 1\frac18$ , option B.