Math & StatisticsFormula-based · Runs in your browser

Logarithm Calculator

Calculate the logarithm of a number with any base.

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Calculation steps

Follow what happened from the selected formula to the displayed answer.

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  1. 1

    Formula selected

    The calculator uses the following formula or method.

    log base b of x = ln(x) ÷ ln(b).

  2. 2

    Values entered

    Your values are placed into the calculation.

    Enter values to see what is used in this step.

  3. 3

    Result calculated

    The formula or method produces the following result values.

    Results will appear after a successful calculation.

  4. 4

    Answer formatted

    Displayed values are rounded and formatted using each output’s configured precision.

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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= Base

    Number · Optional · Default: 10

  • ?number= Number

    Number · Optional · Default: 100

Outputs

1
  • result Result

    Text · 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
Sources
  • No external reference is listed for this calculator. Its formula and variable definitions are shown above.
Limitations
  • Results depend on the selected method and input assumptions. Displayed decimals may be rounded; retain appropriate precision for later calculations.