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4.2.8.3: Exponential_and_Logarithmic_Functions
https://phys.libretexts.org/Courses/Gettysburg_College/Phys_111%3A_Physics_symmetry_and_conservation/04%3A_Miscellanea/4.02%3A_Math_Review/4.2.08%3A_Functions/4.2.8.03%3A_Exponential_and_Logarithmic_Functions
The exponential function $y=b^x$ is increasing if $b>1$ and decreasing if $0<b<1$ . Its domain is $(−∞,∞)$ and its range is $(0,∞)$ . The logarithmic function $y=\log_b(x)$ is the inverse of...The exponential function $y=b^x$ is increasing if $b>1$ and decreasing if $0<b<1$ . Its domain is $(−∞,∞)$ and its range is $(0,∞)$ . The logarithmic function $y=\log_b(x)$ is the inverse of $y=b^x$ . Its domain is $(0,∞)$ and its range is $(−∞,∞)$ . The natural exponential function is $y=e^x$ and the natural logarithmic function is $y=\ln x=\log_e x$ . Given an exponential function or logarithmic function in base $a$ , we can make a change of base to convert this function to a
1.9.14: Exponential and Logarithmic Functions
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/01%3A_Introduction_to_Physics_Measurements_and_Mathematics_Tools/1.09%3A_Math_Review_of_Other_Topics/1.9.14%3A_Exponential_and_Logarithmic_Functions
\(\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ ... $\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ {\text{Take the }\:\log_{b} \text{of each side.}}&{\log_{b}a^{y}=\log_{b}M}\\ {\text{Use the Power Property.}}&{y\log_{b}a=\log_{b}M} \\ {\text{Solve for}\:y. }&{y=\frac{\log_{b}M}{\log_{b}a}} \\ {\text{Substiture}\:y=\log_{a}M.}&{\log_{a}M=\frac{\log_{b}M}{\log_{b}a}} \end{array}$
1.9.14: Exponential and Logarithmic Functions
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_II_(2212)/01%3A_Introduction_to_Physics_Measurements_and_Mathematics_Tools/1.09%3A_Math_Review_of_Other_Topics/1.9.14%3A_Exponential_and_Logarithmic_Functions
\(\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ ... $\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ {\text{Take the }\:\log_{b} \text{of each side.}}&{\log_{b}a^{y}=\log_{b}M}\\ {\text{Use the Power Property.}}&{y\log_{b}a=\log_{b}M} \\ {\text{Solve for}\:y. }&{y=\frac{\log_{b}M}{\log_{b}a}} \\ {\text{Substiture}\:y=\log_{a}M.}&{\log_{a}M=\frac{\log_{b}M}{\log_{b}a}} \end{array}$
2.8.3: Exponential_and_Logarithmic_Functions
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Introductory_Physics_II_(1112)/02%3A_Math_Review/2.08%3A_Functions/2.8.03%3A_Exponential_and_Logarithmic_Functions
The exponential function $y=b^x$ is increasing if $b>1$ and decreasing if $0<b<1$ . Its domain is $(−∞,∞)$ and its range is $(0,∞)$ . The logarithmic function $y=\log_b(x)$ is the inverse of...The exponential function $y=b^x$ is increasing if $b>1$ and decreasing if $0<b<1$ . Its domain is $(−∞,∞)$ and its range is $(0,∞)$ . The logarithmic function $y=\log_b(x)$ is the inverse of $y=b^x$ . Its domain is $(0,∞)$ and its range is $(−∞,∞)$ . The natural exponential function is $y=e^x$ and the natural logarithmic function is $y=\ln x=\log_e x$ . Given an exponential function or logarithmic function in base $a$ , we can make a change of base to convert this function to a

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