Math Doubts


The integral part of a common logarithm is called characteristic.


The logarithm of a quantity is written as integral and fractional forms. The integral part is usually positive, negative or zero. It is called characteristic in logarithms.

$\log{(Q)} \,=\, C + \log{(m)}$

In this case, the literal $C$ represents characteristic and the $\log{m}$ is called mantissa.


If characteristic is negative, then just write magnitude of the characteristic and display a bar over it. It’s mainly to avoid the addition with mantissa and it doesn’t impact the value of the logarithm of a quantity.


$651983$ is a quantity and let’s find characteristic of the logarithm of this number.

$\log{(651983)} \,=\, \log{(6.51983 \times {10}^5)}$

Use product rule of logarithms to express log of product of two or more quantities as sum of their logs.

$\implies$ $\log{(651983)}$ $\,=\,$ $\log{(6.51983)} + \log{({10}^5)}$

Now, use power rule of logarithm to write the logarithm of exponential term as product of two quantities.

$\implies$ $\log{(651983)}$ $\,=\,$ $\log{(6.51983)} + 5\log{(10)}$

The base of common logarithm is $10$. So, the logarithm of $10$ is one as per logarithm of base rule.

$\implies$ $\log{(651983)}$ $\,=\,$ $\log{(6.51983)} + 5 \times 1$

$\implies$ $\log{(651983)}$ $\,=\,$ $\log{(6.51983)} + 5$

$\implies$ $\log{(651983)}$ $\,=\,$ $5+\log{(6.51983)}$

The number $5$ is integrated with log of a quantity and this integral part of logarithm is called characteristic. Therefore, the characteristic of $\log{(651983)}$ is $5$.

Math Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Math Worksheets

The math worksheets with answers for your practice with examples.

Practice now

Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.

Learn more

Math Doubts

A free math education service for students to learn every math concept easily, for teachers to teach mathematics understandably and for mathematicians to share their maths researching projects.

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved