Domain and Range of Logarithmic Functions
Below we will discuss about the domain and range of the logarithmic functions.
Domain of Logarithmic Functions
Domain of the fundamental logarithmic function i.e., y = log x is all the positive real numbers since the logarithmic function is defined for the positive numbers only i.e., x > 0. To find the domain of the other logarithmic functions put the term with log > 0 and find the value of variable.
Domain of the given logarithmic function is given by (value of variable, ∞).
Domain of log x = All Positive Real Numbers
or
Domain of log x = (0, ∞)
Range of Logarithmic Functions
Range of the logarithmic function is defined by putting the different values of x in the given logarithmic functions. The range of the logarithmic function is set of all real numbers.
Range of Logarithmic function = R (Real Numbers)
In summary:
- Domain of log function y = log x is x > 0 (or) (0, ∞)
- Range of any log function is the set of all real numbers (R)
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