Answer
$x=\dfrac{\log34}{\log8}\approx1.695821$
Work Step by Step
$2^{3x}=34$
Apply $\log$ to both sides of the equation:
$\log2^{3x}=\log34$
Using the power of a power rule, we can rewrite the expression on the left side of the equation like this:
$\log(2^{3})^{x}=\log34$
$\log8^{x}=\log34$
The exponent $x$ can be taken down to multiply in front of its respective $\log$:
$x\log8=\log34$
Solve for $x$:
$x=\dfrac{\log34}{\log8}\approx1.695821$
