Log Calculator

Find the logarithm of a number to any base, base 10, base 2, the natural log (base e), or a custom base. Calculates in your browser.

Must be greater than 0.

Logarithm

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Show the math

Any logarithm is the natural log of the value over the natural log of the base:

log_b(x) = ln(x) ÷ ln(b)

The logarithm is the power the base must be raised to in order to reach your number, so log₂(8) = 3 because 2³ = 8. The value must be positive and the base positive and not 1. All math runs locally in your browser.

What this does

A log calculator finds the logarithm of a number to a base you choose, base 10 (common log), base 2, base e (the natural log, ln), or any custom base. The logarithm answers "what power must the base be raised to in order to get this number?"

How to use it

  1. Enter the number (it must be greater than 0).
  2. Choose a base, or enter a custom one.
  3. Read the logarithm.

How it works

Any logarithm is found by dividing the natural log of the value by the natural log of the base. The base must be positive and not equal to 1, and the value must be positive.

log_b(x) = ln(x) ÷ ln(b)

Understanding your result

The logarithm is the exponent that turns the base into your number, so log₂(8) = 3 because 2³ = 8. Logarithms below zero mean the value is smaller than 1, and a value equal to the base always gives 1. The log of any positive number to its own base is the power, which is why logs turn multiplication into addition.

Example

log₁₀(1000) = 3, log₂(8) = 3, and ln(e) = 1.

Sources & methodology

Last updated .

Frequently asked questions

What is a logarithm?

It is the inverse of exponentiation, the power a base must be raised to in order to reach a number. Since 2³ = 8, log base 2 of 8 is 3.

What is the natural log?

The natural log (ln) is a logarithm to the base e ≈ 2.71828. It appears throughout growth, decay, and calculus problems.

Why must the input be positive?

Logarithms are only defined for positive numbers, and the base must be positive and not 1. Zero and negatives have no real logarithm.

Is my data stored?

No. Everything is calculated locally in your browser.