Logarithm Calculator (Any Base)

About this calculator

This calculator finds the logarithm of a number to any base using the change-of-base formula, log_b(x) = ln(x) / ln(b) (equivalently log₁₀(x)/log₁₀(b)), which lets any base be computed from the natural or common log functions built into every calculator and programming language. The result answers the question "to what power must b be raised to get x?" — for example log₂(8) = 3 because 2³ = 8.

Computer scientists use base-2 logarithms constantly to reason about binary search depth and algorithmic complexity, audio and RF engineers use base-10 logs for decibel scales, and chemistry students use them for pH and pOH. Because textbooks and problems set logs in whatever base fits the context, this calculator handles the general case rather than being locked to base 10 or base e.