A logarithm answers the question: to what power must the base be raised to get this number. Log base 10 of 1,000 is 3, because 10 to the power of 3 is 1,000. It is the reverse of an exponent.

What is the natural log?

The natural log, written ln, is the logarithm to base e, where e is about 2.718. It appears throughout maths, science, and finance, especially in growth and decay. The calculator shows it alongside log base 10.

Logarithm Calculator

This calculator finds the logarithm of any number to any base, along with two commonly used variants: the natural log (ln) and log base 10. A logarithm answers a simple question: what power must the base be raised to, to produce this number. It is the mirror image of an exponent, and understanding it helps with science and engineering formulas, interest rate maths, and data analysis. You enter two figures: the number you want the logarithm of, and the base you want to use. As soon as you type, the calculator works out the answer using the change of base rule, dividing the natural log of the number by the natural log of the base, and displays the result under a clear label showing exactly which log you have calculated, for example log base 2 of 1,000. Alongside the main result, it also shows the natural log and the log base 10 of your number, so you can compare all three at once without re-entering anything. The number must be greater than zero, and the base must be positive and cannot equal one, since logarithms are undefined outside these limits, and the calculator will flag it if either rule is broken. Try it with the default values of 1,000 and base 10 to see how the familiar result of 3 is produced, then swap in your own figures.

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Number

Base

logarithm

Natural log (ln)0

Log base 100

How it works

The calculator uses the change of base rule: the log of a number to a base is the natural log of the number divided by the natural log of the base. The number must be greater than zero, and the base must be positive and not equal to one.

Worked example

Log base 10 of 1,000 is 3, because 10 cubed is 1,000. The natural log of 1,000 is about 6.908, and log base 2 of 1,000 is about 9.966.

Related calculators

Exponent Calculator: the reverse of logs.
Square Root Calculator: roots of a number.
Scientific Calculator: advanced functions.
Rule of 72 Calculator: doubling time.

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