The natural logarithm, log base e ≈ 2.71828.

Logarithm Rules

Product, quotient, power and change-of-base rules for logarithms.

lo g_{b} (x y) = lo g_{b} x + lo g_{b} y,; lo g_{b} \frac{x}{y} = lo g_{b} x - lo g_{b} y,; lo g_{b} x^{k} = k lo g_{b} x

Variables

Logarithms turn multiplication into addition. The change of base formula $lo g_{b} x = \frac{l n x}{l n b}$ lets you evaluate any logarithm.

$lo g_{2} 32 - lo g_{2} 4 = lo g_{2} 8 = 3$ .

Evaluate logarithms in any base and solve logarithmic equations step by step.

Exponent Rules

The laws for multiplying, dividing and raising powers.