Answer
$x =\dfrac{\log{3}}{\log{4}} - 7
\\x \approx -6.2075$
Work Step by Step
Take the common logarithm of both sides to have:
$\log{4^{x+7}}=\log{3}$
Apply the power property of logarithms to have:
$(x+7)(\log{4}) = \log{3}$
Divide $\log{4}$ to both sides to have:
$\\x+7 = \dfrac{\log{3}}{\log{4}}$
Subtract $7$ to both sides to have:
$\\x =\dfrac{\log{3}}{\log{4}} - 7
\\x \approx -6.2075$
