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Free online logarithm calculator for ln, log₁₀, log₂ & custom base. Get instant results with step-by-step solutions and antilog calculations!
Must be positive (x > 0)
A logarithm is the inverse of exponentiation. If b^y = x, then log₍b₎(x) = y. It answers: "To what power must we raise b to get x?"
Natural logarithm uses base e (≈2.71828). Essential in calculus, continuous growth, and natural phenomena. Used extensively in advanced mathematics.
Common logarithm uses base 10. Used in pH, Richter scale, decibels, and scientific notation. Default "log" on most calculators.
pH scale: pH = -log₁₀[H⁺]. Measures acidity/alkalinity of solutions.
Richter scale for earthquakes. Each unit = 10x increase in amplitude.
Decibels (dB) measure sound intensity using logarithmic scale.
Algorithm complexity, binary search, information theory (bits).
Compound interest, continuous growth, investment calculations.
Population growth, bacterial growth, radioactive decay.
Stellar magnitude scale, measuring brightness of stars.
Log transformations, data normalization, regression analysis.
Choose from Common Log (log₁₀), Natural Log (ln), Binary Log (log₂), or Custom Base.
Input the positive number (x) for which you want to calculate the logarithm. Must be greater than 0.
If using custom base, enter the base value (b). Must be positive and not equal to 1.
Click Calculate to get instant results with logarithm value, antilog verification, and step-by-step solution.
Unlike basic calculators, we support ln, log₁₀, log₂, and custom base - all in one place.
Detailed explanations showing exactly how the logarithm is calculated, not just the answer.
Automatic antilog calculation to verify results - a feature missing in most calculators.
Comprehensive guide with properties, rules, and real-world applications explained clearly.
Results shown in full precision, scientific notation, and rounded formats for convenience.
Perfect experience on mobile, tablet, and desktop - works seamlessly on all devices.