If {log _{10}}3 = 0.477,the number of digits | vedclass

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(C) Let $y = 3^{40}$.Taking $\log_{10}$ on both sides,we get $\log_{10} y = \log_{10} (3^{40})$.Using the property $\log(a^b) = b \log a$,we have $\lo

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(C) Let $y = 3^{40}$.Taking $\log_{10}$ on both sides,we get $\log_{10} y = \log_{10} (3^{40})$.Using the property $\log(a^b) = b \log a$,we have $\log_{10} y = 40 	imes \log_{10} 3$.Given $\log_{10} 3 = 0.477$,so $\log_{10} y = 40 	imes 0.477 = 19.08$.The number of digits in $3^{40}$ is given by $\lfloor \log_{10} y floor + 1$.Here,$\lfloor 19.08 floor + 1 = 19 + 1 = 20$.Therefore,the number of digits is $20$.

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

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