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  • 14.1: Algebraic Properties of exp and log
    https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Tradler_and_Carley)/14%3A_Properties_of_Exponentials_and_Logarithms/14.01%3A_Algebraic_Properties_of_exp_and_log
    \(\begin{aligned}\log _{2}\left(\sqrt[3]{\dfrac{x^{2}}{y \sqrt{z}}}\right) &=\log _{2}\left(\left(\dfrac{x^{2}}{y \cdot z^{\frac{1}{2}}}\right)^{\frac{1}{3}}\right)=\dfrac{1}{3} \log _{2}\left(\dfrac{...\(\begin{aligned}\log _{2}\left(\sqrt[3]{\dfrac{x^{2}}{y \sqrt{z}}}\right) &=\log _{2}\left(\left(\dfrac{x^{2}}{y \cdot z^{\frac{1}{2}}}\right)^{\frac{1}{3}}\right)=\dfrac{1}{3} \log _{2}\left(\dfrac{x^{2}}{y \cdot z^{\frac{1}{2}}}\right) \\ &=\dfrac{1}{3}\left(\log _{2}\left(x^{2}\right)-\log _{2}(y)-\log _{2}\left(z^{\frac{1}{2}}\right)\right) \\ &=\dfrac{1}{3}\left(2 \log _{2}(x)-\log _{2}(y)-\dfrac{1}{2} \log _{2}(z)\right) \\ &=\dfrac{2}{3} \log _{2}(x)-\dfrac{1}{3} \log _{2}(y)-\dfrac{1}{…
  • 1.5: Exponential and Logarithmic Functions
    https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/01%3A_Critical_Concepts_for_Calculus/1.05%3A_Exponential_and_Logarithmic_Functions
    In this section, we review exponential and logarithmic functions. In addition, we spend time to review the critical Laws of Logarithms and introduce the number e.
  • A.5: Exponential and Logarithmic Functions
    https://math.libretexts.org/Courses/Cosumnes_River_College/Math_400%3A_Calculus_I_-_Differential_Calculus/05%3A_Appendix/5.05%3A_A.5-_Exponential_and_Logarithmic_Functions
    In this section, we review exponential and logarithmic functions. In addition, we spend time to review the critical Laws of Logarithms and introduce the number e.

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