Logarithm Calculator

Logarithms quantify exponential scaling across diverse scientific fields: the Richter earthquake scale, decibels for acoustic sound pressure, pH in chemistry, and algorithmic complexity (O(log n)) in computer science.

This calculator computes logarithmic functions for any positive real argument and positive base (b ≠ 1). It displays the natural log, decimal log, binary log, and custom base evaluation alongside inverse verification via exponentiation.

Using the fundamental change-of-base identity, log_b(a) = ln(a) / ln(b). The engine evaluates native IEEE 754 natural logarithms with double-precision accuracy, reporting errors when arguments or bases violate domain constraints (x ≤ 0 or b ≤ 0 or b = 1).