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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