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1.5: Exponential and Logarithmic Functions

https://math.libretexts.org/Courses/Reedley_College/Calculus_I_(Casteel)/01%3A_Functions_and_Graphs/1.05%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

1.6: Exponential and Logarithmic Functions

https://math.libretexts.org/Courses/Borough_of_Manhattan_Community_College/MAT301_Calculus_I/01%3A_Review-_Functions_and_Graphs/1.06%3A_Exponential_and_Logarithmic_Functions

We use the properties of these functions to solve equations involving exponential or logarithmic terms, and we study the meaning and importance of the number

$e$ .We also define hyperbolic and invers...We use the properties of these functions to solve equations involving exponential or logarithmic terms, and we study the meaning and importance of the number

$e$ .We also define hyperbolic and inverse hyperbolic functions, which involve combinations of exponential and logarithmic functions. (Note that we present alternative definitions of exponential and logarithmic functions in the chapter Applications of Integrations, and prove that the functions have the same properties with either definiti…

1.5: Exponential and Logarithmic Functions

https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Professor_Dean)/1%3A_Functions_and_Graphs_(Review)/1.5%3A_Exponential_and_Logarithmic_Functions

We use the properties of these functions to solve equations involving exponential or logarithmic terms, and we study the meaning and importance of the number

$e$ .We also define hyperbolic and invers...We use the properties of these functions to solve equations involving exponential or logarithmic terms, and we study the meaning and importance of the number

$e$ .We also define hyperbolic and inverse hyperbolic functions, which involve combinations of exponential and logarithmic functions. (Note that we present alternative definitions of exponential and logarithmic functions in the chapter Applications of Integrations, and prove that the functions have the same properties with either definiti…

1.7: Hyperbolic Functions

https://math.libretexts.org/Courses/Cosumnes_River_College/Math_400%3A_Calculus_I_-_Differential_Calculus/01%3A_Critical_Concepts_for_Calculus/1.07%3A_Hyperbolic_Functions

The material in this section is likely not review. Instead, it introduces an important family of functions called the hyperbolic functions. These functions are used throughout calculus and differentia...The material in this section is likely not review. Instead, it introduces an important family of functions called the hyperbolic functions. These functions are used throughout calculus and differential equations.

1.6: Exponential and Logarithmic Functions

https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q1/01%3A_Functions_and_Graphs/1.06%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

1.6: Exponential and Logarithmic Functions

https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_2410%3A_Calculus_1_(Beck)/01%3A_Functions_and_Graphs/1.06%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

1.6: Exponential and Logarithmic Functions

https://math.libretexts.org/Courses/City_University_of_New_York/Calculus_I_(CUNY)/01%3A_Functions_and_Graphs/1.06%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

1.6: Exponential and Logarithmic Functions

https://math.libretexts.org/Courses/Chabot_College/MTH_1%3A_Calculus_I/01%3A_Functions_and_Graphs/1.06%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

1.6: Exponential and Logarithmic Functions

https://math.libretexts.org/Courses/Laney_College/Math_3A%3A_Calculus_1_(Fall_2022)/01%3A_Functions_and_Graphs/1.06%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

1.6: Exponential and Logarithmic Functions

https://math.libretexts.org/Courses/SUNY_Geneseo/Math_221_Calculus_1/01%3A_Functions_and_Graphs/1.06%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

1.6: Exponential and Logarithmic Functions

https://math.libretexts.org/Courses/Coastline_College/Math_C180%3A_Calculus_I_(Tran)/01%3A_Functions_and_Graphs/1.06%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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