Logarithm Calculator

Calculate the logarithm of a positive value for any positive base other than one using the change-of-base identity.

Calculate a logarithm with a custom base

310 raised to this result equals 1000 within floating-point precision.

How this tool works

A logarithm answers which exponent applied to a chosen base produces a target value. This calculator supports arbitrary valid bases by dividing natural logarithms, exposing a general relationship rather than limiting the interface to base ten.

The change-of-base identity gives log base b of x as ln(x)/ln(b). The value and base must be positive, and base one is invalid because every power of one remains one.

How to use it

  1. Enter a positive target value.
  2. Enter a positive logarithm base other than one.
  3. Read the resulting exponent and use the explanation to check it against the original value.

Worked examples

Base ten

Input
Value 1,000, base 10
Output
3

Ten raised to the third power equals one thousand, so the base-ten logarithm of one thousand is exactly three.

Base two

Input
Value 32, base 2
Output
5

Two multiplied by itself five times equals 32, making five the exponent represented by the base-two logarithm.

Limitations

  • The calculator returns real logarithms only.
  • Floating-point rounding can approximate irrational results.