If ${log}_{10} 3 = 0.477$ , the number of digits in $3^{40}$ is.

18

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19

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20

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21

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Solution

The correct option is C $20$
${log}_{10} 3 = 0.477$
$\Rightarrow 3 = 10^{0.477}$
$\Rightarrow 3^{40} = 10^{(0.477)} \times 40$
$3^{40} = 10^{0.477 \times 40}$
$= 10^{19.080} = 10^{19.1}$
$∴$ There are $19$ digits

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