🪵
Log (Logarithm) Calculator
Evaluate logarithms for any base using the change-of-base formula.
Logarithm Calculator —logb(x)
Solve common logarithm log₁₀, natural logarithm ln (logₑ), binary log₂, and arbitrary custom bases.
📐 Fundamental Logarithm Identities & Laws
Change of Base Rule
logb(x) =
ln(x) / ln(b) =
log₁₀(x) / log₁₀(b)
Allows computing arbitrary base logarithms using standard natural or base-10 functions.
Product Rule
logb(x · y) = logb(x) + logb(y)
The log of a product equals the sum of the individual logarithms.
Quotient Rule
logb(x / y) = logb(x) − logb(y)
The log of a ratio equals the numerator log minus denominator log.
Power Rule
logb(xn) = n · logb(x)
Exponents on the argument can be brought to the front as multipliers.