+283 Solve for the sum of all possible values of x when 3^(x^2 + 4x + 4) = 9^(x+2).
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
