How to use: Calculate logarithms (inverse of exponentiation - "what power gives this result?"). Select Type: Natural Log ln (base e≈2.718), Common Log log₁₀ (base 10), or Custom Base. Enter Number (>0). For custom, enter Base. Results show logarithm value. Formula: log_b(x) = y means b^y = x. Examples: log₁₀(100) = 2 (because 10² = 100), ln(e) = 1, log₂(8) = 3 (because 2³ = 8). Properties: log(a×b) = log(a) + log(b), log(a/b) = log(a) - log(b). Applications: pH calculations (acidity), Richter scale (earthquakes), decibels (sound), information theory, exponential decay/growth analysis. Essential for calculus, science, and engineering.