Question

Find the inverse function of f(x)=2^x

Answer 1

lets see if it exists first.

\(\large\color{black}{ y=a^x }\)

\(\large\color{black}{ x=a^y }\)

\(\large\color{black}{ \ln(x)=\ln(a^y) }\)

\(\large\color{black}{ \ln(x)=y\ln(a) }\)

\(\large\color{black}{ \ln(x)\div \ln(a)=y }\)

Answer 2

yes, it is a possibility:)

Answer 3

Thought I'd mention some rules that solomon took

To find the inverse:

Replace f(x) with y
Switch x's and y's, so put x where y is and x where y is.
Solve for y
Replace y with f^-1(x)

Answer 4

you just need to do the same, but with a 2, not with "a".
And notate your inverse not with y, but with \(\large\color{black}{ f^{-1}(x) }\).

Answer 5

Steps I should say haha

Answer 6

yes lol, the steps: I used to just write the steps, but it almost never works...

Answer 7

:P

Answer 8

I think every time I've written the steps to follow, only 1 or 2 people fully understood haha. I always look for who understands it right away and give them props :d

Answer 9

I am sure this posted will come back when she can. She is not going to just leave openstudy if the help is given 20 minutes later. Will see what she says, she should be able to get it:

I mean then you can still use a formula for changing base.

\(\Large\color{black}{ \frac{\ln(x)}{\ln(a)}=\frac{\log(x)}{\log(a)}=\log_a{x} }\)

Answer 10

oh, I see the bug:) lol jk

Answer 11

Hahaha, I agree

Answer 12

Thanks so much you guys!!! :D You're the best! ^.^

Answer 13

anytime glad that my posts were a satisfactory.

Answer 14

if you have any questions about what is don,e or about why it's done, please ask.

Answer 15

I'll let you know, thank you. I got my answer for now. :)

Answer 16

Sure:) Not a problem!

Answer 17

I was going to make a joke about your display picture and ln but it was terrible