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
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 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 logarithm of zero is not defined.
Therefore,
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:
| 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 logy 64 = 2
Solution:
Given that, logy 64 = 2
According to the definition of the logarithm function,
if logab = 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.
More Topics Related to Log 0 Value |
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|---|---|
| Value of Log e | Value of Log Infinity |
| Value of log 10 | Value of Log 1 |
