[tex]\bf y=e^{-x^2}\impliedby \textit{let's take \underline{ln} to both sides}\\\\
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\textit{Logarithm Cancellation Rules}\\\\
log_{{ a}}{{ a}}^x\implies x\qquad \qquad
{{ a}}^{log_{{ a}}x}=x\\\\
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ln(y)=ln(e^{-x^2})\iff log_e(y)=log_e(e^{-x^2})\implies log_e(y)=-x^2
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-ln(y)=x^2\implies \sqrt{-ln(y)}=x[/tex]
