Math Doubts

Characteristic

The integral part of a common logarithm is called characteristic.

Introduction

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.

Note

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.

Example

$651983$ 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 Doubts

A best free mathematics education website for students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

Learn how to solve the maths problems in different methods with understandable steps.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2021 Math Doubts, All Rights Reserved