Question

How many digits are there in the integral part of the numbers whose logarithms are respectively
$4{}^{.}30103,1{}^{.}4771213,3{}^{.}69897,{}^{.}56515?$

Answer 1

The characteristic of logarithm of a number $N>1$ is one less than the number of digits in the number $N$

Characteristics of numbers whose logarithms are $$4.30103,1.4771213,3.69897,0.56515$ are

$4,1,3,0$ respectively.

Hence the number of digits in the integral part of these numbers would be one greater than the characteristic i.e $5,2,4,1$