Answer
$\frac{1}{3}log_2(\frac{8}{5})\approx0.226$
Work Step by Step
Step 1. $2^{3x}=\frac{8}{5} \longrightarrow 3x=log_2(\frac{8}{5}) \longrightarrow x=\frac{1}{3}log_2(\frac{8}{5})$
Step 2. $x=\frac{1}{3}log_2(\frac{8}{5})=log_2(\frac{2}{\sqrt[3] 5})=1-log_2(\sqrt[3] 5)=1-\frac{log(\sqrt[3] 5)}{log2}\approx0.226$
Step 4. Check answers, $x=\frac{1}{3}log_2(\frac{8}{5})\approx0.226$ fits the original equation.
