The given equation
[tex]e^{(2-3x)}=125[/tex]Insert ln on both sides
[tex]ln(e^{2-3x})=ln125[/tex]Use the power rule
[tex](2-3x)ln(e)=ln(125)[/tex]Substitute ln(e) by 1
[tex]2-3x=ln(125)[/tex]Subtract 2 from each side
[tex]\begin{gathered} 2-2-3x=-2+ln(125) \\ \\ -3x=-2+ln(125) \end{gathered}[/tex]Multiply all terms by -1
[tex]3x=2-ln(125)[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{3x}{3}=\frac{2-ln(125)}{3} \\ \\ x=\frac{2-ln(125)}{3} \\ \\ x\approx-0.943 \end{gathered}[/tex]