To solve the expression:
[tex]3+4e^{x+1}=11[/tex]
The first step is to leave the exponential term alone on the left side of the equation:
-Pass 3 to the right side by applying the opposite operation to both sides of it:
[tex]\begin{gathered} 3-3+4e^{x+1}=11-3 \\ 4e^{x+1}=8 \end{gathered}[/tex]
-Divide both sides by 4
[tex]\begin{gathered} \frac{4e^{x+1}}{4}=\frac{8}{4} \\ e^{x+1}=2 \end{gathered}[/tex]
-To take the x-term from the exponent place, apply the natural logarithm to both sides of the expression
[tex]\begin{gathered} \ln (e^{x+1})=\ln 2 \\ x+1=\ln 2^{} \end{gathered}[/tex]
-Finally, pass 1 to the right sides of the expression by applying the opposite operation to both sides of the equal sign:
[tex]\begin{gathered} x+1-1=\ln 2-1 \\ x=\ln (2)-1 \end{gathered}[/tex]
The correct option is the first one.
