Calculate logarithms with any base. Supports natural log (ln), common log (log₁₀), binary log (log₂), and custom base.
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Calculate logarithms instantly with our comprehensive calculator. Find ln (natural log), log10 (common log), log2 (binary log), or logarithm with any custom base. Perfect for mathematics, science, and engineering.
A logarithm is the inverse operation of exponentiation. log_b(x) = y means b^y = x. For example, log10(100) = 2 because 10^2 = 100. Common types include natural log (ln, base e ≈ 2.718), common log (log10), and binary log (log2). Logarithms are essential in science, engineering, and finance.
Logarithm Change of Base
log_b(x) = ln(x) / ln(b)Solve for time in compound interest and population models.
Sound intensity uses logarithmic scale (dB = 10×log10).
Calculate pH = -log10[H+] for acid-base chemistry.
Binary logarithms for algorithm complexity analysis.
ln (natural log) uses base e ≈ 2.71828, while log (common log) uses base 10. In some contexts, 'log' without a base can mean natural log, but in calculators and most applications, log means base 10.