Edit: I just rewrote the whole question, to make it clear, what I'm looking for. Originally I asked about solving $16^{x+1} = 4^{x+3}$, then corrected it to $16^{x+2} = 4^{x+3}$.
But what I really want to know is this: How do you get from
$(x + 2)\ln(16) - (x + 3)\ln(4) = \ln(1)$
to
$x = \frac{3\ln(4) - 2\ln(16)}{\ln(16) - \ln(4)}$
I'm particularly concerned about the factors $(x+2)$ and $(x+3)$ as I don't understand, how they lead up the the last term above.