Question

Find the number of digits in ${875}^{16}$, given $\log 2=.3010300,\log 7=.8450980$.

Answer 1

Given : $\log 2=.3010300,\log 7=.8450980$ ..... $\left(i\right)$
Consider, $\log \left(875{)}^{16}\right)=16\log (7\times 125)$
$=16(\log 7+3\log 5)$
$=16(\log 7+3-3\log 2)$
$=16\times 2.9420080$
$=47.072128$;
Hence the number of digits is $48$.