Log Rules Explorer

Interactive reference for the fundamental laws of logarithms.

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Rule Demonstration

Formulalog_b(M · N) = log_b(M) + log_b(N)

Example

log₂(8 · 4) = log₂(32) = 5
log₂(8) + log₂(4) = 3 + 2 = 5

Understanding these rules helps simplify complex algebraic expressions before solving them.

About this calculator

Logarithm Rules

Logarithms follow specific algebraic rules that simplify complex calculations involving exponents. These rules are derived from the laws of exponents.

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Pro Tips

Product Rule: log(xy) = log(x) + log(y)
Quotient Rule: log(x/y) = log(x) - log(y)
Power Rule: log(x^p) = p·log(x)

Fun Facts

"Logarithms transformed multiplication into addition, simplifying navigation calculations for centuries."
"The slide rule is a mechanical application of log rules."
"Napier invented logarithms in 1614."

Formula: log_b(xy) = log_b(x) + log_b(y)