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.

Latest Math Topics

Latest Math Problems

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

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

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

Copyright © 2012 - 2021 Math Doubts, All Rights Reserved