Question

Given, ${\log }_{10}2=0.3010,{\log }_{10}3=0.4771$. Find the number of digits in $6^{15}$.

• A. $140$
• B. $47$
• C. $12$
• D. none of these

Answer 1

The correct option is C $12$

Let $y=6^{15}$
$\Rightarrow \log y=\log 6^{15}\Rightarrow \log y=15\log 6=15\left(\log 3+\log 2\right)=15(0.3010+0.4771)=15\left(0.7781\right)=11.6715\Rightarrow \log y=11.6715$
{Note : Assume base of the log to be 10, whenever not mentioned }