Answer
$\text{Exact: } \dfrac{\ln 1.6}{3 \ln 2 }$
$\text{Approximately: } 0.226$
Work Step by Step
Divide both sides of the equation by 5:
$$2^{3x}= \dfrac{8}{5} $$
$$2^{3x} = 1.6$$
$\because a^y = b \text{ is equivalent to } y = \log_a b$
$\therefore 2^{3x} = 1.6 \text{ is equivalent to }3x = \log_2 1.6$
Solve the equation above using the Change of Base Formula, which is $\hspace{20pt} \log_ a M = \dfrac{\log_b M}{\log_b a}$, to obtain:
$3x=\log_2 1.6 \\\\
3x= \dfrac{\ln 1.6}{\ln 2}\\\\
\dfrac{3x}{3}= \dfrac{\frac{\ln 1.6}{\ln 2}}{3}\\\\
x = \boxed{\dfrac{\ln 1.6}{3 \ln 2 } \approx 0.226}$
