Logarithm Calculator
Calculate logarithms with any base. Supports natural log (ln), common log (log₁₀), binary log (log₂), and custom base.
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Logarithm Calculator - Natural, Common & Custom Base
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.
What is a Logarithm?
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)How to Use This Calculator
Logarithm Calculator Applications
Exponential Growth/Decay
Solve for time in compound interest and population models.
Decibel Calculations
Sound intensity uses logarithmic scale (dB = 10×log10).
pH Chemistry
Calculate pH = -log10[H+] for acid-base chemistry.
Computer Science
Binary logarithms for algorithm complexity analysis.
Frequently Asked Questions
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.