Question

Find, by inspection, the characteristics of the logarithms of $21735,23.8,350,.035,.2,.87,.875$.

Answer 1

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

Hence characteristics of the logarithms of $21735,23.8,350$ are $4,1,2$ respectively

The characteristic of logarithm of a number $N<1$ is a negative integer with absolute value, one more than the number of zeros to the right of the decimal place

hence the characteristics of $.035,.2,.87,.875$ are $-2,-1,-1,-1$ respectively.