I've got myself into a Logjam

Question

Express x through A, B, C

A^xB^(1+x)=C^(x+5)

the hint I was given to slove this was "Apply log to both sides and use log(A^m)=m log A"

I've got nothing

Answer 1

We derive from $\log(A^m)=m\log(A),\log(AB)=\log(A)\log(B)$ that $$x\log A+(1+x)\log B=(x+5)\log C$$ Then, we have $$x=\frac{\log B-5\log C}{\log C-\log A-\log B}$$