[tex]1.71[/tex]
1) Solving for x, we can write out the following:
[tex]\begin{gathered} 10(1.5)^{3x}=80 \\ \\ \frac{10\cdot \:1.5^{3x}}{10}=\frac{80}{10} \\ \\ 1.5^{3x}=8 \\ \\ \ln \left(1.5^{3x}\right)=\ln \left(8\right) \\ \\ 3x\ln \left(1.5\right)=\ln \left(8\right) \\ \\ \frac{3x\ln \left(1.5\right)}{3\ln \left(1.5\right)}=\frac{\ln \left(8\right)}{3\ln \left(1.5\right)} \\ \\ x=\frac{\ln \left(2\right)}{\ln \left(1.5\right)} \\ \\ x\approx1.71 \end{gathered}[/tex]
That's the answer: 1.71 (Rounded to the nearest hundredth
