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.
log_b(m × n) = log_b(m) + log_b(n)
log_b(m / n) = log_b(m) - log_b(n)
log_b(m^p) = p × log_b(m)
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 ($b > 0, b \neq 1$).
The notation log usually refers to the common logarithm (base 10), while ln represents the natural logarithm with base e.
Yes. This calculator supports common logarithms, natural logarithms, binary logarithms, and custom positive bases other than 1.
Logarithms are widely used in mathematics, engineering, finance, chemistry, physics, computer science, and data analysis for solving exponential relationships and measuring growth or decay.