Answer
$\displaystyle \{\frac{3-\log_{2}5}{3}\}$ or $\{0.226\}$
Work Step by Step
... Divide with 5
$2^{3x}=\displaystyle \frac{8}{5} \quad $... Apply $\log_{2}$(...) to both sides
... LHS: $\log_{2}2^{3x}=3x\log_{2}2=3x$
... RHS: $\displaystyle \log_{2}\frac{8}{5}=\log_{2}8-\log_{2}5=\log_{2}2^{3}-\log_{2}5=3-\log_{2}5$
$3x=3-\log_{2}5$
$x=\displaystyle \frac{3-\log_{2}5}{3}\approx 0.226$
Solution set: $\displaystyle \{\frac{3-\log_{2}5}{3}\}$ or $\{0.226\}$
