Answer
$x=\dfrac{4}{3}+\dfrac{\log11}{3\log7}\approx1.7441$
Work Step by Step
$7^{3x-4}=11$
Apply $\log$ to both sides of the equation:
$\log7^{3x-4}=\log11$
Take $3x-4$ down to multiply in front of its respective $\log$:
$(3x-4)\log7=\log11$
Solve for $x$:
$3x-4=\dfrac{\log11}{\log7}$
$3x=4+\dfrac{\log11}{\log7}$
$x=\dfrac{4+\dfrac{\log11}{\log7}}{3}$
$x=\dfrac{4}{3}+\dfrac{\log11}{3\log7}\approx1.7441$
