The value of log 0 with base 10 is not defined. In this article, the concepts of how to find the value of log 0 using a common logarithmic function and natural logarithmic functions are explained.
What is the Value of Log 0?
|Log10 0 = Not Defined|
To recall, in Mathematics, the logarithmic function defines an inverse function of exponentiation. The logarithmic function is defined by
- if logab = x, then ax = b
- x is the log of a number ‘b.’
- ‘a’ is the base of a logarithmic function.
Note: The variable “a” should be any positive integer, and a ≠1.
The logarithmic function is classified into two types. They are:
- Common Logarithmic Function – Logarithmic function with base 10
- Natural Logarithmic Function – Logarithmic function with base e
If the logarithmic function uses the base other than 10 or e, change it into either base 10 or base e by applying the change of base rule.
To eliminate the exponential functions, and to find the value of a variable, the log functions are functions.
How to Derive Log100 Value?
The log function of 0 to the base 10 is denoted by “log10 0”.
According to the definition of the logarithmic function,
Base, a = 10 and 10x = b
We know that the real logarithmic function logab is only defined for b>0.
It is impossible to find the value of x, if ax = 0,
i.e., 10x = 0, where x does not exist.
So, the base 10 of a logarithm of zero is not defined.
Log10 0 = Not Defined
Value of ln (0) or loge 0
The natural log function of 0 is denoted by “loge 0”. It is also known as the log function of 0 to the base e. The representation of the natural log of 0 is ln (0)
If, ex =0
There is no number to satisfy the equation when x equals to any value.
Therefore, the value of loge 0 is undefined
loge 0 = ln (0) = Not defined
Log Values from 1 to 10
The logarithmic values from 1 to 10 to the base 10 are:
Ln Values from 1 to 10
The logarithmic values from 1 to 10 to the base e are:
Example Question from Log Values
Question: Find the value of y such that logy 64 = 2
Given that, logx 64 = 2
According to the definition of the logarithm function,
if logyb = x, then
ax = b ….(1)
a = y, b= 64, x = 2
Substitute the values in (1), we get
y2 = 64
Take square roots on both sides,
y = √82
Therefore, the value of y is 8.
Visit BYJU’S- The Learning App to learn the values of natural log and common log, and also watch interactive videos to clarify the doubts.