Value of Log 0

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.

What is the value of Log 0?

In this article, let us discuss how to find the value of log 0 using a common logarithmic function and natural logarithmic functions.

Value of Log10 0

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

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

Solved Problem

Question :

Find the value of y such that logy 64 = 2

Solution:

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.