# Value of Log 0

## Trigonometry # 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?

 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 0.301 Log 3 0.4771 Log 4 0.602 Log 5 0.6989 Log 6 0.7781 Log 7 0.845 Log 8 0.903 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) 1.09861 ln (4) 1.38629 ln (5) 1.60944 ln (6) 1.79176 ln (7) 1.94591 ln (8) 2.07944 ln (9) 2.19722 ln (10) 2.30259

### 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.