Log Calculator – Logarithm Base b of x
Compute logarithms with any positive base. Enter the value (x) and the base (b). The result is the exponent to which b must be raised to equal x.
Log Calculator
Calculate log base b of x. Formula: log_b(x) = ln(x) / ln(b).
Logarithm formula
log_b(x) = ln(x) / ln(b)
The change-of-base formula: log base b of x equals natural log of x divided by natural log of b.
Using logarithms
Logarithms turn multiplication into addition and exponentiation into multiplication. Before calculators, slide rules used logarithms for computation. Today, logarithms appear in decibel scales (sound), pH (acidity), Richter scale (earthquakes), and compound interest formulas.
The natural logarithm (base e) is central in calculus and growth models. Exponential growth and decay use e. The common logarithm (base 10) is used in scientific notation and order-of-magnitude estimates. This calculator supports any positive base, so you can work with base 2 (binary log), base 10, or base e as needed.