Explanation
[tex]2e^{3-3x}+7=31[/tex]
Step 1
subtract 7 in both sides
[tex]\begin{gathered} 2e^{3-3x}+7-7=31-7 \\ 2e^{3-3x}=24 \end{gathered}[/tex]
Step 2
divide both sides by 2
[tex]\begin{gathered} 2e^{3-3x}=24 \\ \frac{2e^{3-3x}}{2}=\frac{24}{2} \\ e^{3-3x}=12 \end{gathered}[/tex]
Step 3
get the ln in both sides
[tex]\begin{gathered} \ln (e^{3-3x})=\ln (12) \\ 3-3x=2.48 \\ \text{subtrac 3 in both sides} \\ 3-3x-3=2.48-3 \\ -3x=\ln (12)-3 \\ \text{Divide both sides by -3} \\ \frac{-3x}{-3}=\frac{\ln (12)-3}{-3} \\ x=\frac{\ln (12)-3}{-3} \end{gathered}[/tex]
