Custom Base Logarithm Solver

About this calculator

Most calculators only have buttons for log base 10 (log) and natural log (ln), so solving log_b(x) for an arbitrary base b relies on the change-of-base formula: log_b(x) = ln(x) / ln(b), or equivalently log(x) / log(b) using base-10 logs. Both give the identical result since the ratio of the two logarithms cancels the base conversion.

Custom-base logarithms come up whenever a problem is naturally expressed in a base other than 10 or e — computer science and information theory work in base 2 (bits), music theory and some acoustics problems use base 2 for octaves, and chemistry and finance occasionally define scales in other bases. Students also hit this constantly in algebra and precalculus courses when solving exponential equations like 5^x = 30, which becomes x = log_5(30) = ln(30)/ln(5).

This calculator takes any base and any value and returns log_b(x) directly, without you having to apply the change-of-base formula by hand.