JAMB 1988 · UME · Q9

Logarithms

If $\log_{10} 2 = 0.3010$ and $\log_{10} 3 = 0.4771$ , evaluate $\log_{10} 4.5$ without using logarithm tables.

Worked solution (try it first)

Write 4.5 using 2 and 3: $4.5 = \frac92 = \frac{3^2}{2}$ .
So $\log 4.5 = 2\log 3 - \log 2$ .
That is $2(0.4771) - 0.3010 = 0.9542 - 0.3010$
$= 0.6532$ , option C.

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