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- https://math.libretexts.org/Courses/Hartnell_College/MATH_25%3A_PreCalculus_(Abramson_OpenStax)/04%3A_Exponential_and_Logarithmic_Functions/4.05%3A_Logarithmic_PropertiesRecall that the logarithmic and exponential functions “undo” each other. This means that logarithms have similar properties to exponents. Some important properties of logarithms are given here.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_165_College_Algebra_MTH_175_Precalculus/04%3A_Exponential_and_Logarithmic_Functions/4.05%3A_Logarithmic_PropertiesLog properties: Properties of One, Inverse Properties, Product, Quotient and Power Rules. Expansion and Condensing of log expressions. Change of Base formula. Applications given formulas involving log...Log properties: Properties of One, Inverse Properties, Product, Quotient and Power Rules. Expansion and Condensing of log expressions. Change of Base formula. Applications given formulas involving logarithms.
- https://math.libretexts.org/Courses/Queens_College/Preparing_for_Calculus_Bootcamp_(Gangaram)/05%3A_Day_5/5.05%3A_Laws_of_Logarithms\[\begin{align*} {\log}_6\left (\dfrac{64x^3(4x+1)}{(2x-1)} \right )&= {\log}_664+{\log}_6x^3+{\log}_6(4x+1)-{\log}_6(2x-1)\qquad \text{Apply the Quotient Rule}\\[4pt] &= {\log}_62^6+{\log}_6x^3+{\log...\[\begin{align*} {\log}_6\left (\dfrac{64x^3(4x+1)}{(2x-1)} \right )&= {\log}_664+{\log}_6x^3+{\log}_6(4x+1)-{\log}_6(2x-1)\qquad \text{Apply the Quotient Rule}\\[4pt] &= {\log}_62^6+{\log}_6x^3+{\log}_6(4x+1)-{\log}_6(2x-1) \qquad \text{Simplify by writing 64 as } 2^6\\[4pt] &= 6{\log}_62+3{\log}_6x+{\log}_6(4x+1)-{\log}_6(2x-1) \qquad \text{Apply the Power Rule} \end{align*}\]
- https://math.libretexts.org/Courses/Highline_College/Math_141%3A_Precalculus_I_(old_edition)/04%3A_Exponential_and_Logarithmic_Functions/4.05%3A_Logarithmic_PropertiesRecall that the logarithmic and exponential functions “undo” each other. This means that logarithms have similar properties to exponents. Some important properties of logarithms are given here.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_372%3A_College_Algebra_for_Calculus_(2e)/04%3A_Exponential_and_Logarithmic_Functions/4.05%3A_Logarithmic_PropertiesThis section explores logarithmic properties, including the product, quotient, and power rules, which simplify logarithmic expressions. It also introduces the change-of-base formula, allowing logarith...This section explores logarithmic properties, including the product, quotient, and power rules, which simplify logarithmic expressions. It also introduces the change-of-base formula, allowing logarithms to be rewritten in different bases. Examples illustrate how to apply these properties to simplify expressions and solve logarithmic equations.
- https://math.libretexts.org/Courses/Quinebaug_Valley_Community_College/MAT186%3A_Pre-calculus_-_Walsh/04%3A_Exponential_and_Logarithmic_Functions/4.05%3A_Logarithmic_PropertiesRecall that the logarithmic and exponential functions “undo” each other. This means that logarithms have similar properties to exponents. Some important properties of logarithms are given here.
- https://math.libretexts.org/Workbench/Book-_Precalculus_I_for_Highline_College_w/Rational_Inequalities_and_Equations_of_Circles/1.04%3A_Exponential_and_Logarithmic_Functions/1.4.06%3A_Logarithmic_PropertiesRecall that the logarithmic and exponential functions “undo” each other. This means that logarithms have similar properties to exponents. Some important properties of logarithms are given here.
- https://math.libretexts.org/Courses/Truckee_Meadows_Community_College/TMCC%3A_Precalculus_I_and_II/Under_Construction_test2_04%3A_Exponential_and_Logarithmic_Functions/Under_Construction_test2_04%3A_Exponential_and_Logarithmic_Functions_4.5%3A_Logarithmic_Properties\[\begin{align*} {\log}_6\left (\dfrac{64x^3(4x+1)}{(2x-1)} \right )&= {\log}_664+{\log}_6x^3+{\log}_6(4x+1)-{\log}_6(2x-1)\qquad \text{Apply the Quotient Rule}\\[4pt] &= {\log}_626+{\log}_6x^3+{\log}...\[\begin{align*} {\log}_6\left (\dfrac{64x^3(4x+1)}{(2x-1)} \right )&= {\log}_664+{\log}_6x^3+{\log}_6(4x+1)-{\log}_6(2x-1)\qquad \text{Apply the Quotient Rule}\\[4pt] &= {\log}_626+{\log}_6x^3+{\log}_6(4x+1)-{\log}_6(2x-1) \qquad \text{Simplify by writing 64 as } 2^6\\[4pt] &= 6{\log}_62+3{\log}_6x+{\log}_6(4x+1)-{\log}_6(2x-1) \qquad \text{Apply the Power Rule} \end{align*}\]
- https://math.libretexts.org/Courses/Highline_College/MATH_141%3A_Precalculus_I_(2nd_Edition)/04%3A_Exponential_and_Logarithmic_Functions/4.06%3A_Laws_of_Logarithms\[\begin{align*} {\log}_6\left (\dfrac{64x^3(4x+1)}{(2x-1)} \right )&= {\log}_664+{\log}_6x^3+{\log}_6(4x+1)-{\log}_6(2x-1)\qquad \text{Apply the Quotient Rule}\\[4pt] &= {\log}_62^6+{\log}_6x^3+{\log...\[\begin{align*} {\log}_6\left (\dfrac{64x^3(4x+1)}{(2x-1)} \right )&= {\log}_664+{\log}_6x^3+{\log}_6(4x+1)-{\log}_6(2x-1)\qquad \text{Apply the Quotient Rule}\\[4pt] &= {\log}_62^6+{\log}_6x^3+{\log}_6(4x+1)-{\log}_6(2x-1) \qquad \text{Simplify by writing 64 as } 2^6\\[4pt] &= 6{\log}_62+3{\log}_6x+{\log}_6(4x+1)-{\log}_6(2x-1) \qquad \text{Apply the Power Rule} \end{align*}\]
- https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/04%3A_Exponential_and_Logarithmic_Functions/4.06%3A_Logarithmic_PropertiesRecall that the logarithmic and exponential functions “undo” each other. This means that logarithms have similar properties to exponents. Some important properties of logarithms are given here.
- https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.05%3A_Exponential_and_Logarithmic_Functions/1.5.06%3A_Laws_of_Logarithms\[\begin{align*} {\log}_6\left (\dfrac{64x^3(4x+1)}{(2x-1)} \right )&= {\log}_664+{\log}_6x^3+{\log}_6(4x+1)-{\log}_6(2x-1)\qquad \text{Apply the Quotient Rule}\\[4pt] &= {\log}_62^6+{\log}_6x^3+{\log...\[\begin{align*} {\log}_6\left (\dfrac{64x^3(4x+1)}{(2x-1)} \right )&= {\log}_664+{\log}_6x^3+{\log}_6(4x+1)-{\log}_6(2x-1)\qquad \text{Apply the Quotient Rule}\\[4pt] &= {\log}_62^6+{\log}_6x^3+{\log}_6(4x+1)-{\log}_6(2x-1) \qquad \text{Simplify by writing 64 as } 2^6\\[4pt] &= 6{\log}_62+3{\log}_6x+{\log}_6(4x+1)-{\log}_6(2x-1) \qquad \text{Apply the Power Rule} \end{align*}\]
