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If $\log_{10} 3 = 0.4771$ , then the number of digits in $81^{35}$ is

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Detailed Solution

$\log_{10} 3 = 0.4771$

Let $k = 81^{35}$

$\log k = 35 \log 81 = 35 \times \log 3^{4}$

$= 140 \log 3$

$= 140 \times 0.4770$

$\log k = 66.794$

The number of digits is 67

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