The value of log 1 to the base 10 is equal to 0. It can be evaluated using the logarithm function, which is one of the important mathematical functions. Log functions are commonly used to solve many lengthy problems and reduce the complexity of the problems by reducing the operations from multiplication to addition and division to subtraction. In this article, we are going to learn and evaluate the value of log 1 for common and natural logarithmic functions.

Logarithmic Functions

Generally, the logarithm is classified into two types. They are

• Common Logarithmic Function (represented as log)
• Natural Logarithmic Function (represented as Ln)

The log function with base 10 is called the common logarithmic functions and the log with base e is called the natural logarithmic function.

The logarithmic function is also defined by,

if log_ab = x, then a^x = b.

Where x is defined as the logarithm of a number ‘b’ and ‘a’ is the base of the log function that could have any base value, but usually, we consider it as ‘e’ or ‘10’ in terms of the logarithm. The value of the variable ‘a’ can be any positive number but not equal to 1 or negative number.

Now let us find out the logarithm value of 1 with the help of logarithm definition.

What is the Value of Log 1?

From the definition of logarithm function,  log_ab = x can be written in the form of an exponential function as given below:

Then, a^x = b

To find the value of log 1, since the base is not defined here, let us consider the base as 10. Hence, we can write log 1 as log₁₀ 1.

Now, from the logarithm definition, we have the value of a = 10 and b = 1. Such that,

log₁₀ x = 1

By the logarithm rule, we can rewrite the above expression as;

10^x = 1

As we know, any number raised to the power 0 is equal to 1. Thus, 10 raised to the power 0 makes the above expression true.

So, 10⁰ = 1

This will be a condition for all the base value of log, where the base raised to the power 0 will give the answer as 1.

Therefore, the value of log 1 is zero.

log₁₀1 = 0

where ‘a’ could be any positive value apart from 1.

What is the value of Ln 1?

Similarly, we can represent the natural logarithm value of 1,i.e. Ln 1.

Ln (b) = log_e (b)

∴ Ln(1) = log_e(1)

Or e^x = 1

∴ e⁰ = 1

Hence, Ln(1) = log_e(1) = 0

Log Values from 1 to 10

The logarithmic values from 1 to 10 to the base 10 are:

Solved Example

Example: Solve log 1 – log 0

Solution: Given, log 1 + log 0

log 1 = 0 and log 0 = -∞

Therefore, log 1 + log 0 = 0 -(-∞) = ∞

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