How do I find the inverse of this exponential function? x=−3(3^(−x))+9

betterthennewzv

betterthennewzv

Open question

2022-08-13

How do I find the inverse of this exponential function?
x = 3 ( 3 x ) + 9
I know the steps up until a certain point.
x = 3 ( 3 y ) + 9
x 9 = 3 ( 3 y )
( x 9 ) 3 = 3 y
l n ( x 9 3 ) = y l n 3
Not sure what to do from here. I know I have to get y by itself but thats it. Can anyone help please?

Answer & Explanation

Brennan Parks

Brennan Parks

Beginner2022-08-14Added 14 answers

Divide both sides by ln 3 and you are there
vroos5p

vroos5p

Beginner2022-08-15Added 5 answers

We want to solve for y, after switching x and y
y = 3 ( 3 x ) + 9
becomes
x = 3 ( 3 y ) + 9 x 9 = 3 ( 3 y ) x 9 3 = 3 y 1 3 x + 3 = 3 y ln ( 1 3 x + 3 ) = ln ( 3 y ) ln ( 1 3 x + 3 ) = y ln 3 ln ( 1 3 x + 3 ) ln 3 = y

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?