What is the number of digits in $5^{40}$ ? (Given $l o g_{10} 2$ = 0.3010)

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Solution

The correct option is A
28

$l o g 5^{40} = 40 l o g 5 = 40 \times [l o g (\frac{10}{2})] = 40 (l o g 10 - l o g 2)$
$= 40 (1 - 0.3010) = 40 \times 0.6990 = 27.96.$
Characteristic = 27. Hence, the number of digits in $5^{40}$ is 28.

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