Logarithm Calculator

Last updated: 2026-08-24

Logarithm Calculator — Calculate logarithms in any base.
Inputs
Result
Enter values and press Calculate

How to use it

  1. Value x = 256, base b = 4
  2. Apply change of base formula: ln(256) ÷ ln(4)
  3. Calculate: 5.5452 ÷ 1.3863
  4. Result: logâ‚„(256) = 4 (since 4⁴ = 256)

Common mistakes

  • ⚠️ Trying to calculate log of negative number or zero
  • ⚠️ Using base = 1 which is undefined
  • ⚠️ Confusing natural log with log base 10

Worked example

Calculate log10(100) and ln(5).

The logarithm {log_val} is the power to which the base must be raised to get x.

Input guide

FieldTypical range
xArgument: 0.0001 to 1e12 (must be positive)
baseBase: 0.0001 to 100 (must be positive, not 1)