What is the change of base formula?

logₐ(x) = log(x) / log(a), where log can be any base. This allows you to compute logarithms in any base using a calculator that only has log (base 10) or ln (base e).

What is the natural logarithm?

The natural logarithm (ln) is a logarithm with base e (Euler's number, approximately 2.71828). It arises naturally in calculus and exponential growth problems.

Algebra

Laws of Logarithms

Formula

logₐ(xy) = logₐ(x) + logₐ(y), logₐ(x/y) = logₐ(x) − logₐ(y), logₐ(xⁿ) = n × logₐ(x)

What is Laws of Logarithms?

Logarithms convert multiplication into addition, division into subtraction, and exponentiation into multiplication. These properties make logarithms essential for simplifying complex calculations.