Question

Find the number of digits in ${875}^{16}$, given $\log 2=0.3010,\log 7=0.8450980$

Answer 1

Let $y={875}^{16}$

$\log y=16\log 875$

$=16\log (7\times 125)$

$=16[\log 7+\log 5^3]$

$=16(\log 7+3\log 5)$

$=47.07$

Hence, number of digit ${875}^{16}$ IS $47$