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 [Top]

\[\log_{2}{9}-\log_{2}{3}\]
1
Use Quotient Rule: \(\log_{b}{\frac{x}{y}}=\log_{b}{x}-\log_{b}{y}\)
\[\log_{2}{\frac{9}{3}}\]

2
Simplify \(\frac{9}{3}\) to \(3\)
\[\log_{2}{3}\]

Done

Decimal Form: 1.584963


 

Example 2 [Top]

\[\log_{3}{4}-\log_{3}{2}\]
1
Use Quotient Rule: \(\log_{b}{\frac{x}{y}}=\log_{b}{x}-\log_{b}{y}\)
\[\log_{3}{\frac{4}{2}}\]

2
Simplify \(\frac{4}{2}\) to \(2\)
\[\log_{3}{2}\]

Done

Decimal Form: 0.630930


 

Example 3 [Top]

\[\log_{2}{a}-\log_{2}{b}\]
1
Use Quotient Rule: \(\log_{b}{\frac{x}{y}}=\log_{b}{x}-\log_{b}{y}\)
\[\log_{2}{\frac{a}{b}}\]

Done