Question

How do you find the inverse of #3^(2x)?

Answer 1

The step by step explanation and working is given below.

Explanation:

To find the inverse of function please follow the following steps.

Step 1: Swap `x` and `y`
Step 2: Solve for `y.`

The final answer would be the inverse function.

Our question `3^(2x)`

`y=3^(2x)`

Step 1: Swap `x` and `y`.
`x=3^(2y)`

Step 2: Solve for `y`

`log_3(x) = 2y` Using If `a=b^c` then `log_b(a) = c`

`1/2log_3(x) = y`
`y=1/2 log_3(x)`
`f^-1(x) =l/2log_3(x)` Answer

If converting logarithm to the exponent form is not clear the following steps might help you understand how it is done.

`log(x) = log(3^2y)`
`log(x) = 2ylog(3)`
`log(x)/(2log(3)) = y`
`1/2(log(x)/log(3)) = y` using change of base rule.
`1/2 log_3(x) = y`
The inverse function `f^-1(x) = 1/2 log_3(x)`