Logarithm Calculator
Calculate logarithms in any base — common, natural and binary logs.
Last updated: August 2026
Result
2
log10(100)
Value
100
Base
10
Logarithms are only defined for positive values and bases.
How it works
log_base(value) = ln(value) ÷ ln(base). Defined only for value > 0 and base > 0, base ≠ 1.
Example: log₁₀(100) = 2; log₂(8) = 3; ln(e) = 1.
Frequently Asked Questions
What is a logarithm?
A logarithm answers the question: to what power must the base be raised to get the value? log₁₀(100) = 2 because 10² = 100.
What is the difference between log, ln and log₂?
Log is base 10 (common), ln is base e ≈ 2.718 (natural), and log₂ is base 2 (binary). They differ only by the base used.
What is the logarithm of zero or a negative number?
Logarithms are only defined for positive values. Log(0) and log of negatives do not exist in real numbers.
Where are logarithms used in daily life?
The pH of water, decibel sound levels, the Richter earthquake scale and medical half-life calculations all use logarithms to compress huge ranges into readable numbers.