Logarithm Calculator

The number and base must be positive; the base cannot equal 1. Use 10 for common logarithms, 2 for binary, or 2.718281828459045 for natural logarithms.

Logarithm

Logarithm
2
log⁡b(x)=ln⁡(x)ln⁡(b)\log_b(x)=\frac{\ln(x)}{\ln(b)}

How it works

Enter a positive number and a positive base other than one. The change-of-base formula computes the real logarithm. Bases between zero and one are also supported.

Example

The base-10 logarithm of 100 is 2, because 10 squared is 100. The base-2 logarithm of 8 is 3.

Frequently asked questions

Can I take the logarithm of zero or a negative number?

Not as a finite real number. This calculator rejects zero and negative arguments and does not compute complex logarithms.

Why is base one not allowed?

Every power of one is one, so there is no unique inverse. Bases close to one can also magnify floating-point rounding.