The natural logarithm of a number is defined as follows:
[tex]\ln A=x_{}[/tex]
means that when we elevate the Euler number e to x, the result is A:
[tex]\ln A=x\Rightarrow A=e^x[/tex]
In this problem, we have
[tex]A=e^{-3}[/tex]
Thus
[tex]\ln e^{-3}=x\Rightarrow e^{-3}=e^x[/tex]
Then, since the bases are the same, for the equation to hold we need the exponents to be the same:
[tex]\begin{gathered} e^{-3}=e^x\Rightarrow-3=x \\ \\ \therefore x=-3 \end{gathered}[/tex]
