Logarithm Calculator
Calculate logarithms for any positive number and valid base, including base 2, base 10, and natural logarithms.
Logarithm Details
Enter a positive number and a valid logarithm base to calculate the logarithm.
The number for which you want to calculate the logarithm. It must be greater than 0.
The base must be greater than 0 and cannot be 1.
Common Bases
How is the logarithm calculated?
A logarithm answers the question: what power should the base be raised to get the number?
For example: log₂(8) = 3 because 2³ = 8.
The calculator uses the change of base method to calculate logarithms for any valid base.
Logarithm Result
Your calculated logarithm will appear here.
Your result will appear here
Enter a number and base, then click Calculate.
What is a Logarithm?
A logarithm tells you the power to which a base must be raised to produce a given number.
For example, log₂(8) = 3 because 2³ = 8.
Logarithm Formula
If bˣ = y, then logᵦ(y) = x.
Example
For log₁₀(100), the answer is 2 because 10² = 100.
Common Logarithms
- Base 10 logarithm is commonly written as log₁₀(x).
- Base 2 logarithm is commonly used in computing and information theory.
- Natural logarithm uses the mathematical constant e as its base and is written as ln(x).
Valid Logarithm Values
The number must be greater than 0. The base must also be greater than 0 and cannot equal 1.