Value of Log 0
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?
Log_{10} 0 = Not Defined 
To recall, in Mathematics, the logarithmic function defines an inverse function of exponentiation. The logarithmic function is defined by:
 if log_{a}b = x, then a^{x} = b
Where,
 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 Log_{10}0 Value?
The log function of 0 to the base 10 is denoted by “log_{10} 0”.
According to the definition of the logarithmic function,
Base, a = 10 and 10^{x} = b
We know that the real logarithmic function log_{a}b is only defined for b>0.
It is impossible to find the value of x, if a^{x} = 0,
i.e., 10^{x }= 0, where x does not exist.
So, the base 10 of logarithm of zero is not defined.
Therefore,
Log_{10} 0 = Not Defined
Value of ln (0) or log_{e} 0
The natural log function of 0 is denoted by “log_{e} 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, e^{x} =0, there is no number to satisfy the equation when x equals to any value.
Therefore, the value of log_{e }0 is undefined
log_{e }0 = ln (0) = Not defined
Log Values from 1 to 10
The logarithmic values from 1 to 10 to the base 10 are:
Log 1  0 
Log 2  0.3010 
Log 3  0.4771 
Log 4  0.6020 
Log 5  0.6989 
Log 6  0.7781 
Log 7  0.8450 
Log 8  0.9030 
Log 9  0.9542 
Log 10  1 
Ln Values from 1 to 10
The logarithmic values from 1 to 10 to the base e are:
ln (1)  0 
ln (2)  0.693147 
ln (3)  1.098612 
ln (4)  1.386294 
ln (5)  1.609438 
ln (6)  1.791759 
ln (7)  1.94591 
ln (8)  2.079442 
ln (9)  2.197225 
ln (10)  2.302585 
Example Question from Log Values
Question: Find the value of y such that log_{y} 64 = 2
Solution:
Given that, log_{y} 64 = 2
According to the definition of the logarithm function,
if log_{a}b = x, then
a^{x} = b ….(1)
a = y, b= 64, x = 2
Substitute the values in (1), we get
y^{2 }= 64
Take square roots on both sides,
y = √8^{2}
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.
More Topics Related to Log 0 Value 


Value of Log e  Value of Log Infinity 
Value of log 10  Value of Log 1 