Quotient Rule

Reference > Algebra: Common Logarithms

Description

The Quotient Rule states that:

\(\log_{b}{\frac{x}{y}}=\log_{b}{x}-\log_{b}{y}\)

Examples

Example 1

\[\log_{2}{9}-\log_{2}{3}\]

Use Quotient Rule: \(\log_{b}{\frac{x}{y}}=\log_{b}{x}-\log_{b}{y}\).

\[\log_{2}{\frac{9}{3}}\]

Simplify \(\frac{9}{3}\) to \(3\).

\[\log_{2}{3}\]

Done

Decimal Form: 1.584963

Example 2

\[\log_{3}{4}-\log_{3}{2}\]

Use Quotient Rule: \(\log_{b}{\frac{x}{y}}=\log_{b}{x}-\log_{b}{y}\).

\[\log_{3}{\frac{4}{2}}\]

Simplify \(\frac{4}{2}\) to \(2\).

\[\log_{3}{2}\]

Done

Decimal Form: 0.630930

Example 3

\[\log_{2}{a}-\log_{2}{b}\]

Use Quotient Rule: \(\log_{b}{\frac{x}{y}}=\log_{b}{x}-\log_{b}{y}\).

\[\log_{2}{\frac{a}{b}}\]

Done