ClarityKitFind a tool
Math

Logarithm Calculator

Find the logarithm of a positive value in a positive base other than one.

Exact method explained belowEditable inputs

Set up your calculation

Runs on your device

SOLUTION

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter value, base.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

log_b(x) = ln(x) ÷ ln(b). This gives the exponent to which b must be raised to produce x.

A WORKED EXAMPLE

log₁₀(1,000) = 3 because 10³ = 1,000.

What to keep in mind

The value and base must be positive, and the base cannot be one. This tool calculates real logarithms only.

Common questions

Can a logarithm be negative?

Yes. In a base greater than one, values between zero and one have negative logarithms.

What happens with base one?

One raised to any power remains one, so the usual logarithm is not defined.

Methodology maintained by ClarityKit. How these tools are built and checked.