we have the exponential equation
[tex]10e^{-3x}=564[/tex]Solve for x
[tex]e^{-3x}=\frac{564}{10}[/tex]Apply ln on both sides
[tex]\ln e^{-3x}=\ln \frac{564}{10}[/tex]Applying property of log
[tex]\begin{gathered} (-3x)\cdot\ln e=\ln \frac{564}{10} \\ \\ (-3x)=\ln \frac{564}{10} \end{gathered}[/tex][tex]x=-\frac{\ln \frac{564}{10}}{3}[/tex]