## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$\text{Exact: } \dfrac{\ln 1.6}{3 \ln 2 }$ $\text{Approximately: } 0.226$
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: $3x=\log_2 1.6 \\\\ 3x= \dfrac{\ln 1.6}{\ln 2}\\\\ \dfrac{3x}{3}= \dfrac{\frac{\ln 1.6}{\ln 2}}{3}\\\\ x = \boxed{\dfrac{\ln 1.6}{3 \ln 2 } \approx 0.226}$