Question

Change y=e^(-x^2) to x=

Answer 1

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