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

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Basic of Logarithms

medium

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

A

$18$

B

$19$

C

$20$

D

$21$

(IIT-1992)

Solution

(c) Let $y = {3^{40}}$

Taking log both the sides, $\log \,y = \log {3^{40}}$

==> $\log \,\,y = 40\,\log 3$$ \Rightarrow \,\,\log \,y = 19.08$

$\therefore$ Number of digits in $y = 19 + 1 = 20$ .

Standard 11

Mathematics

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