Question

Given $\log 10\left(2\right)=0.3010$, the number of digits in ${20}^{64}$ would be:

• A. $121$
• B. $99$
• C. $1$
• D. $84$

Answer 1

The correct option is D $84$

Given that:

${\log }_{10}2=0.3010$

Let $x={20}^{64}$

Taking log both sides, we get

$\log x=\log {20}^{64}$

$\Rightarrow \log x=64\log 20$

$\Rightarrow \log x=64(\log 2+\log 10)$

$\Rightarrow \log x=64(0.3010+1)$

$\Rightarrow \log x=64\times 1.3010$

$\Rightarrow \log x=83.264$

Number of digits in ${20}^{64}=83+1=84$