Question

2^(-x^2)=4

Answer 1

Solve for x:
\[2^{-x ^{2}}=4\]

Answer 2

\[\huge 2^{-x^2} = 4\]
\[\huge x^2 = -\frac{ \ln 4 }{ \ln 2 }\]
after that square both sides.

Answer 3

Yep, you get -2. So you have complex answers. I've been looking at this over and over and they are technically extraneous solutions because you cannot insert those into a logarithm and have it give you an answer.

Answer 4

\[2^{-x ^{2}}=4 or \frac{ 1 }{2^{x ^{2}} }=2^{2},1=2^{x ^{2}}*2^{2}\]
\[2^{x ^{2}+2}=1=2^{0},x ^{2}+2=0,x ^{2}=-2=2\iota ^{2},x=\pm \sqrt{2}\iota \]