JAMB 2015 · UTME · Q35

Logarithms

If $\log_8 10 = x$ , evaluate $\log_8 5$ in terms of $x$ .

Worked solution (try it first)

Write 5 as $\frac{10}{2}$ : $\log_8 5 = \log_8 10 - \log_8 2$ .
$8^{\frac13} = 2$ (the cube root of 8 is 2), so $\log_8 2 = \frac13$ .
So $\log_8 5 = x - \frac13$ , option C.

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