Math Doubts

Limits of logarithmic functions

There are two fundamental properties of limits to find the limits of logarithmic functions and these standard results are used as formulas in calculus for dealing the functions in which logarithmic functions are involved.

$(1) \,\,\,$ $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{\log_{e}{(1+x)}}{x}}$ $\,=\,$ $1$

The limit of quotient of natural logarithm of $1+x$ by $x$ is equal to one.

$(2) \,\,\,$ $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{\log_{b}{(1+x)}}{x}}$ $\,=\,$ $\dfrac{1}{\log_{e}{b}}$

The limit of ratio of logarithm of $1+x$ to a base to $x$ is equal to reciprocal of natural logarithm of base.


Let’s learn how to use these two limits formulas for the logarithmic functions in finding the limits of functions in which logarithmic functions are involved.

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