The given equation is:
ln (x + 2) = -5
Take the exponent of both sides
[tex]e^{\ln (x+2)\text{ }}=e^{-5}[/tex]The exponential cancels the ln on the Left Hand Side:
[tex]\text{x + 2 = e}^{-5}[/tex]Subtract 2 from both sides:
[tex]\begin{gathered} \text{x + 2 - 2 = e}^{-5}-2 \\ x=e^{-5}-2 \end{gathered}[/tex]