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Calculate logarithms for any base, natural log ln(x), and base 10 log10(x) instantly with formulas and step-by-step guidance.
Compute logarithm log_b(x) for any custom base, as well as natural log (ln), common log (log10), and binary log (log2).
A logarithm answers the question: To what power must we raise the base b to get the value x?
log_b(x · y) = log_b(x) + log_b(y)log_b(x / y) = log_b(x) - log_b(y)log_b(x^k) = k · log_b(x)log_b(b) = 1 and log_b(1) = 0log_b(x) = y ⇔ b^y = xThe exponent to which base b must be raised to produce x.log_b(x) = ln(x) / ln(b)Used to compute logarithms for arbitrary bases.log_10(100) = 2 because 10^2 = 100. log_2(8) = 3 because 2^3 = 8.
A logarithm is the inverse operation to exponentiation. It calculates the exponent to which a base must be raised to produce a given number.
log usually refers to base 10 (common logarithm), while ln refers to base e (natural logarithm, where e ≈ 2.71828).