Quotient Rule

Reference > Algebra: Common Logarithms

Description

The Quotient Rule states that:

log⁡bxy=log⁡bx−log⁡by\log_{b}{\frac{x}{y}}=\log_{b}{x}-\log_{b}{y}
Examples

Example 1

log⁡29−log⁡23\log_{2}{9}-\log_{2}{3}
1
Use Quotient Rule: log⁡bxy=log⁡bx−log⁡by\log_{b}{\frac{x}{y}}=\log_{b}{x}-\log_{b}{y}.
log⁡293\log_{2}{\frac{9}{3}}

2
Simplify  93\frac{9}{3}  to  33.
log⁡23\log_{2}{3}

Done

Decimal Form: 1.584963


 

Example 2

log⁡34−log⁡32\log_{3}{4}-\log_{3}{2}
1
Use Quotient Rule: log⁡bxy=log⁡bx−log⁡by\log_{b}{\frac{x}{y}}=\log_{b}{x}-\log_{b}{y}.
log⁡342\log_{3}{\frac{4}{2}}

2
Simplify  42\frac{4}{2}  to  22.
log⁡32\log_{3}{2}

Done

Decimal Form: 0.630930


 

Example 3

log⁡2a−log⁡2b\log_{2}{a}-\log_{2}{b}
1
Use Quotient Rule: log⁡bxy=log⁡bx−log⁡by\log_{b}{\frac{x}{y}}=\log_{b}{x}-\log_{b}{y}.
log⁡2ab\log_{2}{\frac{a}{b}}

Done


 
Cymath foriOSAndroid