Question

8e^3x+9=13. Round to the nearest thousandth

Answer 1

\[ 8e^{3x}+9=13\\
8e^{3x}=4\\
e^{3x}=\frac{4}{8}=\frac{1}{2}\\
\ln(e^{3x})=\ln\left( \frac{1}{2}\right)=-\ln 2\\
3x(\ln e)=-\ln 2\\
3x=-\ln 2\\ \, \\
x = \frac{-\ln 2}{3}\approx-0.231\]