Answer
$x =\dfrac{\log{2}}{\log{6}} - 3
\\x \approx -2.6131$
Work Step by Step
Take the common logarithm of both sides to have:
$\log{(6^{x+3})}=\log{2}$
Apply the power property of logarithms to have:
$(x+3)(\log{6}) = \log{2}$
Divide $\log{6}$ to both sides to have:
$\\x+3 = \dfrac{\log{2}}{\log{6}}$
Subtract $3$ to both sides to have:
$\\x =\dfrac{\log{2}}{\log{6}} - 3
\\x \approx -2.6131$
