Calculators

Logarithm

Take the logarithm of a value in any base plus its natural log (ln). For pH, decibels, information theory and exponential growth.

Try it now

💡 Good to know: Logarithms turn multiplication into addition — the trick behind slide rules, and why decibels and the Richter scale are logarithmic.

Worked example

log: 3 · ln: 6.907755

How it’s solved

Worked on the example above, step by step — follow along and you can do it on paper next time, no tool required.

A logarithm asks “what exponent turns the base into this value?” Any base is found with change-of-base using natural logs.
Change of base: log_b(x) = ln(x) ÷ ln(b)
ln(1000) ÷ ln(10) = 3
The natural log (ln) is simply log base e
ln(1000) = 6.907755

Learn the method

Inputs

Value
1000
Base
10

Frequently asked

What is log base 10 of 1000?

3, and its natural log (ln) is about 6.9078.

How is an arbitrary base computed?

By the change-of-base rule: log_b(x) = ln(x) ÷ ln(b).