Introduction to Domain of a Logarithmic Function
In general, let us consider a function, y = f(x).
It means, y the value of the function varies depending upon the input variable x and nature of the function.
As long as any value of x makes gives a real value of y, the function said to exist all the time. But this may not be the case with many functions due to the nature and restriction of the functions. In such a case, only for a particular set (or sets) of values of the input variable the function exists.
The set (or sets) of values of the input variable which makes the function exist is called the domain of the function and the corresponding set (or sets) of values of the function is called as the range of the function.
Let study the domain of a logarithmic function.
Description of a Domain of a Logarithmic Function
Before determining the domain of a logarithmic function, let us see what a logarithmic function is.
Mathematicians discovered that the function could be described in the form
f(x) = logbx, which is called as logarithmic function.
Let, n = logbx Then as per the definition of a logarithmic function, bn = x
Determining the Domain of a Logarithmic Function
To determine the domain of a logarithmic function, let us start from the fundamental concept.
Let us take the simple form of a logarithmic function y = logbx
Then as per definition by = x
I am planning to write more post on Definite Integrals, Newton Raphson Method. Keep checking my blog.
If you carefully notice, the value of x becomes closer and closer to 0 as y becomes infinitely smaller and smaller. As ultimate, only when y becomes – infinity, the value of x becomes 0, which is an impossible situation. The following graph shows the variation.
Reversing the above argument, it can be said that a logarithmic function exists only for all values greater than 0.
That is domain of a logarithmic function is x > 0
Please note that for simplicity we assumed f(x) = logbx. In general it could be a logarithmic function of another function of x.
That is, f(x) = logb g(x).
In such a case, the domain of the logarithmic function is determined by solving g(x) > 0
For example, if f(x) = logb (x – 1), then the domain of the function is x > 1.
In general, let us consider a function, y = f(x).
It means, y the value of the function varies depending upon the input variable x and nature of the function.
As long as any value of x makes gives a real value of y, the function said to exist all the time. But this may not be the case with many functions due to the nature and restriction of the functions. In such a case, only for a particular set (or sets) of values of the input variable the function exists.
The set (or sets) of values of the input variable which makes the function exist is called the domain of the function and the corresponding set (or sets) of values of the function is called as the range of the function.
Let study the domain of a logarithmic function.
Description of a Domain of a Logarithmic Function
Before determining the domain of a logarithmic function, let us see what a logarithmic function is.
Mathematicians discovered that the function could be described in the form
f(x) = logbx, which is called as logarithmic function.
Let, n = logbx Then as per the definition of a logarithmic function, bn = x
Determining the Domain of a Logarithmic Function
To determine the domain of a logarithmic function, let us start from the fundamental concept.
Let us take the simple form of a logarithmic function y = logbx
Then as per definition by = x
I am planning to write more post on Definite Integrals, Newton Raphson Method. Keep checking my blog.
If you carefully notice, the value of x becomes closer and closer to 0 as y becomes infinitely smaller and smaller. As ultimate, only when y becomes – infinity, the value of x becomes 0, which is an impossible situation. The following graph shows the variation.
That is domain of a logarithmic function is x > 0
Please note that for simplicity we assumed f(x) = logbx. In general it could be a logarithmic function of another function of x.
That is, f(x) = logb g(x).
In such a case, the domain of the logarithmic function is determined by solving g(x) > 0
For example, if f(x) = logb (x – 1), then the domain of the function is x > 1.
