What is the number of digits in 540? (Given log102 = 0.3010)

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Question

What is the number of digits in

5^{40}

? (Given

l o g_{10} 2

= 0.3010)

Options:

A . 28

B . 27

C . 14

D . 13

Answer: Option A
:
A

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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