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.
$x^2 \cdot 2^{x + 1} +2 ^{\lvert x - 3\rvert + 2}
 = x^2 \cdot 2^{\lvert x - 3\rvert + 4} + 2^{x - 1}$
$(x^2 - 7x + 5)^{x^2-2x-15} = 1$

1) Making $2^{x-1}=a$ and $2^{|x-3|+2}=b$ you have $$4ax^2+b=4bx^2+a\iff(4x^2-1)(a-b)=0$$ This gives $x=\frac 12$ and $x\ge3$
2) You have two independent possibilities $$x^2-7x+5=1\\x^2-2x-15=0$$
