Inverse of g(x)= ln(2x+12)?

I have no idea :/
I'm using MyMaths doing questions from it, but it doesn't help you when you're stuck, so I'm left not knowing what to do.

Inverse of g(x)=ln(2x+12)

Given y, how do you find out what x is? (A formula for x, if you like)

Eg with a simpler example, if y = lnx, what's the inverse of that?

I know that the inverse of y = lnx is y=e^x and if I were to use an example of:

y = e^x-2 then invese of y = ln(x-2)
because y-2=e^x therefore ln(x-2)=x
but my brain can't translate the other question.

I think you swapped a 3 for a 2 there but no worries.


So you have y = ln(2x+12), so the first step is to try and isolate the 2x+12.. how can you do that?

Yea, sorry :P Getting late and not as concentrated as I should be.

Get the inverse of it? I think I've done it...

I did e^y=e^[ln(2x+12)]
e=2x+12
x=(e-12)/2
x=(1/2) - 6 ???

Pretty close. Don't let the e^y disappear though. And you've turned e/2 into 1/2 somehow but that should be 0.5e^y - 6, then you're fine. (maybe swap the y and x with x and f^-1(x) respectively as well)

Thanks Sean and Ash : )

Yea, I'm confusing myself a bit too much and muddling things up.

I was using MyMaths and it accepeted 1/2 :/ I guess I may be confusing myself again. I know that e = 2.718...., so e/2 can't be 0.5, is it an error on the websites part or (most likely) an error from my understanding of it and my rearrangement?

https://gyazo.com/b9835dc854ba25decd41c5e0810df100