Question

So for the variable. leave your answer in its exact form

Answer 1

Step-by-step explanation

`2e^(3-3x)+7=31`

Step 1

subtract 7 in both sides

`\begin{gathered} 2e^(3-3x)+7-7=31-7 \\ 2e^(3-3x)=24 \end{gathered}`

Step 2

divide both sides by 2

`\begin{gathered} 2e^(3-3x)=24 \\ (2e^(3-3x))/(2)=(24)/(2) \\ e^(3-3x)=12 \end{gathered}`

Step 3

get the ln in both sides

`\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} \\ (-3x)/(-3)=(\ln (12)-3)/(-3) \\ x=(\ln (12)-3)/(-3) \end{gathered}`