Question 173557: 3^(x^2+20)=(1/27)^(3x)
Answer by nycsub_teacher(90)   (Show Source):
You can put this solution on YOUR website! 3^(x^2+20)=(1/27)^(3x)
The idea is to get the same base on both sides of the exponential equation.
We can express 1/27 as 3^(-3) because they both mean the same thing.
We now have this:
3^(x^2+20)= [3^(-3)]^(3x)
Do you see that we now have the same base 3 on both sides?
We now bring down the exponents and set them them equal to each other.
Before we do that, [3^(-3)]^(3x)becomes 3^(-9x). Do you see how this happened?
3^(x^2 + 20) = 3^(-9x)
x^2 + 20 = -9x
x^2 + 9x + 20 = 0
We now have a quadratic equation that can be factored.
(x + 4) (x + 5) = 0
Set each factor equal to zero and solve for x.
x + 4 = 0
x = -4
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x + 5 = 0
x = -5
Did you follow?
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