Answer
$x=0.449$
$x=-4.449$
Work Step by Step
$\log_6(x+2)-\log_6x=\log_6(x+5)$
$\log_6(\frac{x+2}{x})=\log_6(x+5)$
Using the one-to-one property:
$\frac{x+2}{x}=x+5$
$x+2=x^2+5x$
$0=x^2+4x-2~~$ ($a=1,b=4,c=-2$):
$x=\frac{-b±\sqrt {b^2-4ac}}{2a}=\frac{-4±\sqrt {4^2-4(1)(-2)}}{2(1)}=\frac{-4±\sqrt {24}}{2}=\frac{-4±2\sqrt 6}{2}=-2±\sqrt 6$
$x=-2+\sqrt 6=0.449$
or
$x=-2-\sqrt 6=-4.449$
