Answer
$x =\dfrac{\frac{\log{11}}{\log{7}}+4}{3} \approx 1.7441$$
Work Step by Step
Take the common logarithm of both sides to have:
$\log{(7^{3x-4})}=\log{11}$
Apply the power rule to have:
$(3x-4)\log{7}=\log{11}$
Divide $\log{7}$ to both sides to have:
$3x-4=\dfrac{\log{11}}{\log{7}}
\\3x=\dfrac{\log{11}}{\log{7}}+4
\\x =\dfrac{\frac{\log{11}}{\log{7}}+4}{3} \approx 1.7441$
