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Calculate logarithms in any base, antilogarithms, and change of base conversions. Supports common log (base 10), natural log (ln), and binary log (base 2).
A logarithm is the inverse operation of exponentiation. The logarithm base b of a number x (written logᵦ(x)) is the exponent to which b must be raised to produce x. Common bases include 10 (common log), e (natural log), and 2 (binary log).
Calculate logᵦ(x) — to what power must the base be raised to get x?
| Expression | Value |
|---|---|
| log₁₀(1) | 0 |
| log₁₀(10) | 1 |
| log₁₀(100) | 2 |
| log₂(8) | 3 |
| log₂(256) | 8 |
| ln(1) | 0 |
| ln(e) | 1 |
| ln(10) | 2.30259 |
Formula
logₐ(x) = ln(x) / ln(a)x = the number (argument) — must be positive
a = the base — must be positive and not equal to 1
ln = natural logarithm (base e ≈ 2.71828)
Worked Example
Calculate log₂(64)
Did you know? John Napier invented logarithms in 1614 to simplify complex calculations. Before electronic calculators, logarithm tables and slide rules were essential tools for scientists, engineers, and navigators for over 350 years (source: Mathematical Association of America).
Sources
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