Equation which has to be solved with logarithms I need some help how to solve these equations for $x$. I think I have to use logarithms but still not sure how to do it and would be really grateful if someone could explain me.
$x^2 \cdot 2^{x + 1} +2 ^{\lvert x - 3\rvert + 2}
 = x^2 \cdot 2^{\lvert x - 3\rvert + 4} + 2^{x - 1}$
$(x^2 - 7x + 5)^{x^2-2x-15} = 1$

Hint: if
\begin{equation*}
  (x^2 - 7x + 5)^{\color{blue}{x^2 - 2x - 15}} = 1,
\end{equation*}
what do you think $\color{blue}{x^2 - 2x - 15}$ is equal to?
This is merely one of the three possibilities. For all of them, please check out fleablood's answer.
