Question

Which Function is the inverse of the exponential function y= (3/2)^x ?

Answer 1

Explanation:

To find the inverse of the exponential function y = (3/2)^x, we need to interchange the roles of x and y, and then solve for y.

So, starting with y = (3/2)^x, we can write:

x = (3/2)^y

To solve for y, we can take the logarithm of both sides with base 3/2:

log(3/2) x = y

Therefore, the inverse of the exponential function y = (3/2)^x is:

y = log(3/2) x

or in exponential form:

y = (log base 3/2) x

This function is the logarithmic function with base 3/2.

Answer 2

The exponential function
`y=\left((3)/(2)\right)^x` has an inverse function denoted as
`\log _(3 / 2)(x)`. Therefore, the correct option is C.

To find the inverse function of the exponential function
`y=\left((3)/(2)\right)^x` , you can interchange x and y and solve for the new y. The inverse function is denoted as
`y^(-1)`.

Starting with the original function:

`y=\left((3)/(2)\right)^x`

Interchanging x and y:

`x=\left((3)/(2)\right)^y`

Now, solve for y:

`y=\log _{(3)/(2)}(x)`

So, the correct answer is C.