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: 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 \log_a(xy) = \log_a(x) + \log_a(y) }
• Quotient rule: 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 \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