Logarithms Practice Test 2

Question : 32 of 39

Marks: +1, -0

Given

\log_10 2 = 0.3010

, what is the number of digits in

20^64

Solution:

Let,

x = (20)^64

⇒ x = (2 × 10)^64

⇒ \log x = 64 \log2 + 64 \log10

⇒ \log x = 64 × 0.3010 + 64 × 1

= 19.2640 + 64 = 83.2640

Hence, the required number of digits

= 83 + 1 = 84

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