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

To find the inverse of (3^{2x}), we first express the function in terms of (y):

[ y = 3^{2x} ]

Then, we interchange the variables (x) and (y):

[ x = 3^{2y} ]

Next, we solve this equation for (y):

[ \log_3(x) = 2y ]

[ y = \frac{1}{2} \log_3(x) ]

So, the inverse function of (3^{2x}) is (f^{-1}(x) = \frac{1}{2} \log_3(x)).

By signing up, you agree to our Terms of Service and Privacy Policy

The step by step explanation and working is given below.

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

The final answer would be the inverse function.

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

By signing up, you agree to our Terms of Service and Privacy Policy

- How do you find the asymptotes for #f(x) = (x+3)/(x^2 + 8x + 15)#?
- How do you determine if #y=1-sin(x)# is an even or odd function?
- How do you find the inverse of #y=cos x +3 # and is it a function?
- If a function of the form #y=ax^2+k# has an #x#-intercept of 7.5, what is the other #x#-intercept?
- How do you find the compositions given #f(x)=8x# and #g(x)=x/8#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7