Logarithm Calculator

Last updated: 2026-08-24

Logarithm Calculator — Logarithm Calculator. Free online calculator with formula, examples and step-by-step guide.
Inputs
Result
Enter values and press Calculate

How to use it

  1. {'step': 1, 'description': 'Identify number (1000) and base (10)'}
  2. {'step': 2, 'description': 'Find x where 10ˣ = 1000'}
  3. {'step': 3, 'description': 'Since 10³ = 1000, logâ‚\x81â‚€(1000) = 3'}
  4. {'step': 4, 'description': 'Natural log: ln(1000) = 6.9078'}

Common mistakes

  • ⚠️ Trying to calculate log of zero or negative numbers (undefined)
  • ⚠️ Using base 1 which is mathematically invalid for logarithms
  • ⚠️ Confusing log base 10 with natural log (base and)

Worked example

Calculate log base 10 of 1000 for pH or Richter scale calculations

The result ({result}) is the exponent to which base_log must be raised to get number; log_natural us is base and (Euler's number).

Input guide

FieldTypical range
numeroMust be positive; typical: 0.001-1,000,000
base_logCommon: 10 (common log), e≈2.718 (natural), 2 (binary); cannot be 0 or 1