What is the change of base formula?

log_b(x) = ln(x) / ln(b). It lets you compute any logarithm with a calculator that only has ln or log.

Logarithm Calculator

Evaluate log_b(x) for any base, including the natural log (base e) and common log (base 10). Exact values are recognized when the argument is a power of the base.

How to use the logarithm calculator

Enter the base (use e for natural log).
Enter the argument (must be positive).

Examples

log₂ 64

Answer: 6

ln e³

Answer: 3

Formulas

Logarithm Rules

lo g_{b} (x y) = lo g_{b} x + lo g_{b} y,; lo g_{b} \frac{x}{y} = lo g_{b} x - lo g_{b} y,; lo g_{b} x^{k} = k lo g_{b} x