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Solve for the sum of all possible values of x when 3^(x^2 + 4x + 4) = 9^(x+2).

 Apr 19, 2019
 #1
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Solve for x :
3^(x^2 + 4 x + 4) = 9^(x + 2)

Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):
log(3) (x^2 + 4 x + 4) = 2 log(3) (x + 2)

Divide both sides by log(3):
x^2 + 4 x + 4 = 2 (x + 2)

Expand out terms of the right hand side:
x^2 + 4 x + 4 = 2 x + 4

Subtract 2 x + 4 from both sides:
x^2 + 2 x = 0

Factor x from the left hand side:
x (x + 2) = 0

Split into two equations:
x = 0 or x + 2 = 0
Subtract 2 from both sides:
x = 0     or     x = -2

 Apr 20, 2019
 #2
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Thank you!

 Apr 26, 2019

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