I am finding this problem confusing :
If,for all $x$,$f(x)=f(2a)^x$ and $f(x+2)=27f(x)$,then find $a$.
When $x=1$ I have that $f(1)=f(2a)$ using the first identity.
Then when $x=2a$ I have by the second identity that $f(2a+2)=27f(2a)$,after that I simple stare at the problem without having a clue of how to proceed.
What's the trick the problem is calling for ?
I've thought of finding the inverse of the function $f(x)$ but It's not really clear to me how to apply this idea as I don't have linear functions .
Can you guys give me a hint ?