Properties of Logarithmic Function

The properties of the logarithmic functions help us to solve the logarithmic functions. The several properties of logarithmic functions are listed below:

  • logb1 = 0
  • logb b = 1
  • logb (pq) = logb p + logb q
  • logb (p/q) = logb p – logb q
  • logb px = x logb p
  • logb p = (logc p) / (logc b)

Logarithmic Function

Logarithmic functions are the function that represents the inverse of the exponential functions. The functions that include logarithms are called the logarithmic function. Concept of logarithm in mathematics is used for changing multiplication and division problems to problems of addition and subtraction.

In this article, we will learn about logarithmic functions, the domain and range of logarithmic functions, properties of logarithmic functions, logarithmic graphs and others in detail.

Table of Content

  • What are Logarithmic Functions?
  • Domain and Range of Logarithmic Functions
  • Logarithmic Graph
  • Properties of Logarithmic Functions
  • Derivative of Logarithmic Functions
  • Integral of Logarithmic Functions

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What are Logarithmic Functions?

Logarithmic functions are referred to as the inverse of the exponential function. In other words, the functions of the form f(x) = logbx are called logarithmic functions where b represents the base of the logarithm and b > 0....

Domain and Range of Logarithmic Functions

Below we will discuss about the domain and range of the logarithmic functions....

Logarithmic Function​ Graph

We know that, logarithmic functions are the inverse of the exponential functions. So, the graph of both the functions are symmetrical about line y = x. Also, the domain of the logarithmic function log x is set of all the positive real numbers and the range is the set of all real numbers....

Properties of Logarithmic Function

The properties of the logarithmic functions help us to solve the logarithmic functions. The several properties of logarithmic functions are listed below:...

Derivative of Logarithmic Function

The derivative of logarithmic function logex is 1/x. The derivative of the logarithmic function with base ‘a’ i.e., logax is 1 / (x ln a). The formula for derivatives of logarithmic function is given below....

Integral of Logarithmic Function

Integral of logarithmic function is calculated using the ILATE rule. The value of the integral of the logarithmic functions given below....

Examples on Logarithmic Functions

Example 1: Evaluate log 20 – log 2...

Practice Questions on Logarithmic Functions

Q1: Evaluate: log 5 + log 12....

FAQs on Logarithmic Functions

What is the Logarithmic Function?...

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