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

3 Answers | Add Yours

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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

Top Answer

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

This is an exponential equation.

We notice that the bases from the both sides are matching, so we'll use the one to one property of exponential functions:

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

We'll move all terms to one side:

-x^2+3x+4 = 0

We'll multiply by (-1):

x^2 - 3x - 4 = 0

We'll apply the quadratic formula:

x1 = [3+sqrt(9+16)]/2

x1 = (3+5)/2

x1 = 4

x2 = (3-5)/2

x2 = -1

We'll check the solutions into the original equation:

e^(-x1^2)=e^(-3x1-4) for x1 = 4

e^(-16)=e^(-12-4)

e^(-16) = e^(-16)

e^(-x2^2)=e^(-3x2-4) for x2 = -1

e^(-1)=e^(3-4)

e^(-1)=e^(-1)

So, both solution are admissible!

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

e^(-x^2) = e^(-3x-4). To solve for x.

Both sides of the equation are the exponent of the same base. So the exponents -x^2 on left and the exponent -3x-4 should be equal for for the equality.

-x^2 = -3x-4. Multiply by -1.

x^2 =3x+4

x^2-3x-4 =0

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

x-4 =0 or x+1 = 0

x=4 or x =-1.

We’ve answered 318,983 questions. We can answer yours, too.

Ask a question