Logarithmic Properties

Logarithmic Properties

• Equality rule: If $\log _{a}(x)=\log _{a}(y)$, then Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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