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e^(-x^2) = e^(-3x-4)

We know that:

if e^a = e^b

==> a = b

Since the bases are equals, then the powers should be equal.

=Therefore,

-x^2 = -3x - 4

==> x^2 - 3x - 4 = 0

Factor:

==> (x-4)(x+1) = 0

Then we have two solutions:

==> ...

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e^(-x^2) = e^(-3x-4)

We know that:

if e^a = e^b

==> a = b

Since the bases are equals, then the powers should be equal.

=Therefore,

-x^2 = -3x - 4

==> x^2 - 3x - 4 = 0

Factor:

==> (x-4)(x+1) = 0

Then we have two solutions:

==> x1= 4

==> x2= -1

Approved by eNotes Editorial Team