Math Doubts

Logarithm of one Rule

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


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


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.

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


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

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

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

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

$(4) \,\,\,\,\,\,$ $\log_{\displaystyle e} 1 = 0$

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

Math Doubts
Math Doubts is a free math tutor for helping students to learn mathematics online from basics to advanced scientific level for teachers to improve their teaching skill and for researchers to share their research projects. Know more
Follow us on Social Media
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.

Learn more