Answer
$x=\dfrac{\log2}{\log6}-3\approx-2.6131$
Work Step by Step
$6^{x+3}=2$
Apply $\log$ to both sides of the equation:
$\log6^{x+3}=\log2$
Take $x+3$ down to multiply in front of its respective $\log$:
$(x+3)\log6=\log2$
Solve for $x$:
$x+3=\dfrac{\log2}{\log6}$
$x=\dfrac{\log2}{\log6}-3\approx-2.6131$
