How it works
Calculate the logarithm of a number with any base.
Input query strings and outputs
Use an input name in this page’s URL as ?name=value, and join additional inputs with &. Portable shared links may instead use the compact ?ac= state parameter.
Input query strings
2-
?base=BaseNumber · Optional · Default: 10
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?number=NumberNumber · Optional · Default: 100
Outputs
1-
resultResultText · Primary output
result contains the calculator’s complete rendered result area, including its visible result cards, tables, charts, and messages.
Calculate logs for any base (10, e, 2, and more)
Description
The Logarithm Calculator is a specialized math tool that solves the inverse of exponential functions. Given a base and a number, it determines the exponent to which the base must be raised to produce that number. It includes convenient buttons for the most common logarithm types used in science, finance, and engineering.
Inputs
- Base Presets: Quick buttons for Base 10 (Common Log), Base e (Natural Log), and Base 2 (Binary Log).
- Custom Base: Enter any positive number (not equal to 1).
- Number (x): The value you want to find the log of.
Outputs
- Result: The calculated exponent (logarithm) with 5-decimal precision.
Chart
- N/A: This tool provides direct numeric logarithmic results.
“Good to Know”
- Natural Log (ln): The natural logarithm uses the base e (Euler’s number, approx. 2.718). It is fundamental in calculus and radioactive decay calculations.
- Log Constraints: Logarithms are only defined for positive numbers and positive bases that are not 1.
- Base 10: If you see a log without a specified base in a textbook, it almost always refers to Base 10.
Examples
Example 1: Common Log
- Input: Base: 10, Number: 1000
- Output: 3.00000
Example 2: Natural Log
- Input: Base: e, Number: 10
- Output: 2.30259
Example 3: Binary Log
- Input: Base: 2, Number: 1024
- Output: 10.00000