Arithmetic & Number Theory

Logarithm Base n

Logarithm of x to an arbitrary base.

Formula

Formula
log_b(x) = ln xln b

Variables

SymbolDefinitionType & rangeUnitsRole
x input (> 0) real number (ℝ) input
b base (> 0, ≠ 1) real number (ℝ) input

Try it yourself

Interactive calculator
Result

Worked examples

Example 1
Givenx = 81, base b = 3
Result4
Example 2
Givenx = 1000, base b = 10
Result3