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  4. If log 2=0.301, then find the number of digits in 21024.

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

Logarithms

Solution:

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 .