Question 173557
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?