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

Find the logarithm of a number to any base. Enter the number and the base, and the calculator shows the log, along with the natural log and the log base 10. A logarithm is the reverse of a power: it tells you the exponent the base needs to reach the number.

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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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