Answer
$x=\dfrac{4}{3}+\dfrac{\log15}{3\log3}\approx2.15$
Work Step by Step
$3^{3x-4}=15$
Apply $\log$ to both sides of the equation:
$\log3^{3x-4}=\log15$
Take the exponent on the left side of the equation down to multiply in front of its respective $\log$:
$(3x-4)\log3=\log15$
Take $\log3$ to divide the right side:
$3x-4=\dfrac{\log15}{\log3}$
Take $4$ to the right side:
$3x=4+\dfrac{\log15}{\log3}$
Take $3$ to divide the right side:
$x=\dfrac{4}{3}+\dfrac{\log15}{3\log3}\approx2.15$
