Logarithm Calculator
Calculate common logarithm (log₁₀), natural logarithm (ln), and custom base logarithm with step-by-step calculation process.
Enter Value
Enter a number to calculate its logarithm.
Result
Common Logarithm Result
2
Calculation Steps
log₁₀(100)
Common logarithm (base 10)
2
10^x = 100
Find x such that 10^x equals the number
2
Logarithm Type Comparison
log₁₀
Common Log
2
ln
Natural Log
4.605170186
log₂
Base 2
6.64385619
Logarithm Formulas Reference
Definitions and formulas for logarithm functions.
log₁₀(x)
Common logarithm: Logarithm with base 10
Example: log₁₀(100) = 2 (10² = 100)
ln(x)
Natural logarithm: Logarithm with base e(≈2.71828)
Example: ln(e) = 1, ln(1) = 0
log_b(x) = ln(x) / ln(b)
Change of base formula: Logarithm for any base b
Example: log₂(8) = ln(8) / ln(2) = 3 (2³ = 8)
Logarithm Calculator Guide
Logarithm is the inverse operation of exponentiation. log_b(x) represents "what power should b be raised to get x". All calculations are performed in your browser. No data is sent to any server.