Log Calculator

Calculate logarithms with custom bases, natural logarithms ($\ln$), common logarithms ($\log_{10}$), or solve logarithmic equations.

Logarithm Calculator

Calculate logarithm logb(x) for any base b.

Logarithm Rules & Formulas

A logarithm is the inverse function to exponentiation. If by = x, then logb(x) = y.

Product Rule: log_b(m × n) = log_b(m) + log_b(n)
Quotient Rule: log_b(m / n) = log_b(m) - log_b(n)
Power Rule: log_b(m^p) = p × log_b(m)
Change of Base: log_b(x) = ln(x) / ln(b)

Frequently Asked Questions (FAQs)

Natural Logarithm ($\ln$) is a logarithm with base $e$ (Euler's number, $\approx 2.718281828$).

In real-number mathematics, logarithms are only defined for positive arguments ($x > 0$) and positive bases ($b > 0, b \neq 1$).