Logarithm Calculator — log₁₀, ln, log₂, Any Base

公式

How this is calculated

The logarithm log_b(x) answers the question "b raised to what power equals x?" For the common log (base 10), log₁₀(100) = 2 because 10² = 100. For the natural log, the base is Euler's number e ≈ 2.71828, and ln(x) appears constantly in calculus, growth models, and probability. For the binary log (base 2), log₂(8) = 3 because 2³ = 8 — this arises in computer science (bits, binary tree depth, information theory).

All logarithm values are computed from the natural logarithm using the change-of-base rule: log_b(x) = ln(x) / ln(b). For a custom base, enter any positive number except 1 — base 1 is excluded because 1 raised to any power equals 1, making the logarithm undefined. The stat panel always shows common, natural, and binary logs alongside the selected-base result so you can compare all three.

The input must be strictly positive; the logarithm of zero is negative infinity, and the logarithm of a negative number is not a real number (it is defined in the complex plane, but not on the real line). The plot shows the log curve up to about 1.6× your input, letting you see its characteristic shape — fast growth near zero, then gradually flattening — and exactly where your point lies.