# Logarithm of one Rule

A mathematical rule of determining the value of logarithm of one is called log one rule.

## Formula

$\large \log_{b}{1} = 0$

### Proof

The value of log of 1 can be derived mathematically by considering the zero exponent rule.

#### Apply Power of 0 Rule

$b$ is a literal and $b$ raised to the power of zero is denoted by $b^0$. According to Power of zero rule, the value of $b^0$ is one.

$\large b^0 = 1$

#### Use Relation of Logarithm with Exponents

Logarithm is the inverse operation of the exponential system. So, express exponential equation in logarithmic form.

$\,\,\, \therefore \,\,\,\,\,\,$ $\large \log_{b}{1} = 0$

##### Examples

The base of logarithmic term can be any quantity. The logarithm of one to any number is always zero.

$(1) \,\,\,\,\,\,$ $\log_{1} 1 = 0$

$(2) \,\,\,\,\,\,$ $\log_{2} 1 = 0$

$(3) \,\,\,\,\,\,$ $\log_{10} 1 = 0$

$(4) \,\,\,\,\,\,$ $\log_e} 1 =$

$(5) \,\,\,\,\,\,$ $\log_{5127} 1 = 0$

A best free mathematics education website for students, teachers and researchers.

###### Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

###### Maths Problems

Learn how to solve the maths problems in different methods with understandable steps.

Learn solutions

###### Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.