Given:
Given the exponential function
![f(x)=2^x](https://img.qammunity.org/2023/formulas/mathematics/high-school/4zfs7cmm18gayjob0j01e7yfqa7wstig.png)
and the logarithmic function
![f(x)=\log_2x](https://img.qammunity.org/2023/formulas/mathematics/college/ihibo2pdqfypmj890w6ph4wypjokktw1u0.png)
Required: Compare and contrast the given exponential and logarithmic function.
Step-by-step explanation:
The exponential function
![f(x)=2^x](https://img.qammunity.org/2023/formulas/mathematics/high-school/4zfs7cmm18gayjob0j01e7yfqa7wstig.png)
has real numbers as its domain, but its range is only the positive real numbers, y > 0, since an exponential function never takes a negative value. The graph of it is given below.
The logarithmic function
![y=\log_2x](https://img.qammunity.org/2023/formulas/mathematics/college/r3vpq7enk3opm6z2qh0954lkpm0jbfksq5.png)
where x > 0 is equivalent to the function
![x=2^y](https://img.qammunity.org/2023/formulas/mathematics/college/1hwzb3b69jvwj4f5bt4hfhwfux0r4z4rsh.png)
,that is,
![y=\log_2x](https://img.qammunity.org/2023/formulas/mathematics/college/r3vpq7enk3opm6z2qh0954lkpm0jbfksq5.png)
is the inverse of the function
![y=2^x](https://img.qammunity.org/2023/formulas/mathematics/high-school/pxj2mht7hrddkxaw51sn3i7fw6eifb05uu.png)
The function
![y=\log_2x](https://img.qammunity.org/2023/formulas/mathematics/college/r3vpq7enk3opm6z2qh0954lkpm0jbfksq5.png)
has the domain of set of positive real numbers and the range of set of real numbers. The graph of it is given below.
Since the logarithmic function is the inverse of the exponential function, the domain of logarithmic function is the range of exponential function, and vice versa.