Logarithmic Properties

Logarithmic Properties

• Equality rule: If $\log _{a}(x)=\log _{a}(y)$, then $x=y$
• Product rule: $\log _{a}(xy)=\log _{a}(x)+\log _{a}(y)$
• Quotient rule: $\log _{a}\left({\frac {x}{y}}\right)=\log _{a}(x)-\log _{a}(y)$
• Power rule: $\log _{a}(x^{n})=n\log _{a}(x)$
• Change-of-base rule: $\log _{a}(x)={\frac {\log _{b}(x)}{\log _{b}(a)}}$

Resources

• Logarithmic Properties, Book Chapter
• Guided Notes

Licensing

Content obtained and/or adapted from:

• Logarithms and Exponentials, Wikibooks: A-level Mathematics/OCR/C2 under a CC BY-SA license