Question

If ${\log }_{10}2=0.301$ and ${\log }_{10}11=1.041$, then the number of digits in ${88}^{100}$ is

Answer 1

Let $N={88}^{100}$
Then ${\log }_{10}N={\log }_{10}\left({88}^{100}\right)$
$=100{\log }_{10}(2^3\times 11)$
$=100(3{\log }_{10}2+{\log }_{10}11)$
$=100(3\times 0.301+1.041)$
$=100\times 1.944$
$=194.4$
$\therefore$ Characteristic of ${\log }_{10}N$ is $194$.
Hence, the number of digits in ${88}^{100}$ is$195$.