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1. If $\log 2 = 0.30103,$ the number of digits in $4^{50}$ is -

A. 30

B. 31

C. 100

D. 200

Solution:

\begin{aligned} \log 4^{50} \\ = 50 \log 4 \\ = 50 \log 2^{2} \\ = (50 \times 2) \log 2 \\ = 100 \times \log 2 \\ = (100 \times 0.30103) \\ = 30.103 \\ ∴ characteristic = 30, \end{aligned}

Hence, the number of digits in

4^{50} = 31

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