Question

If $\log 2=0.301$, then find the number of digits in $2^{1024}$.

• A. 307
• B. 308
• C. 309
• D. 310

Answer 1

Answer: (C)

Let $x=2^{1024}$
$\Rightarrow \log x=\log 2^{1024}$
$=1024\log 2=1024(0.301)$
$\Rightarrow \log x=308.22$
$\Rightarrow \text{ The characteristic is }308$
$\therefore$ The number of digits in $2^{1024}$ is 309 .