C3 functions

So I got x=ln(0.5) but this is apparently wrong. I don't even know if this is the correct way to find x or, if it is, where I have gone wrong! A little help please?

I am really stuck on this questions about functions from C3. Could someone help me please?? The actual bit I cannot do is finding the value of x:

f(x)=ln(3-2x) x<1.5
g(x)=e^2x+1
Find the exact value of x for which f^-1(x)=g(x).

So far I have got f^-1(x)= (3-e^x)/2

Then I tried:

(3-e^x)/2 = e^2x+1
3-e^x = 2e^2x+2
0=2e^2x+e^x-1
0=(2e^x-1)(e^x+1)

So I got x=ln(0.5) but this is apparently wrong. I don't even know if this is the correct way to find x or, if it is, where I have gone wrong! A little help please?

Have you copied the question correctly? I don't understand what the < sign is there for

The answer is apparently x=ln2... and the question definitely said x<1.5. The other answer I got for x was ln(-1) which is not a possible answer. Thanks for your help anyway

Really? Try setting x >=1.5 and see what happens to f(x).