How logarithm calculator works
A logarithm answers the question "what power do I raise this base to in order to get this number?" The base-10 log of 1000 is 3, because 10^3 = 1000. The natural log (ln) uses base e (about 2.718) and is central to calculus and exponential growth. The binary log (base 2) appears in computing and information theory.
This calculator uses the change-of-base formula log_b(x) = ln(x) / ln(b), so it works for any positive base other than 1. It defaults to base 10 and recognises the special cases: base 10 reports the common log, base e the natural log, and base 2 the binary log.
Enter a value and a base and the tool returns the logarithm. The value must be positive, and the base must be positive and not equal to 1. Use it for algebra homework, science, decibel and pH calculations (which use log10), and bit-depth or doubling-time problems (which use log2).