Advanced Hard!!!!

[Dragonballful23]

Determine what x equals.


9^(x+2)=3^x

[eliseo]

It's infinity

[Dragonballful23]

Originally Posted by eliseo

It's infinity

Here is how you solve. since 9^(x+2)=3^x, you can say 3^(2x+4)=3^x

Now, just like when you factor quadratic equations, take out the 3.
3x+4=x
2x=-4
x=-2!

[coolbro]

Now, just like when you factor quadratic equations, take out the 3.
3x+4=x
2x=-4
x=-2!

[MAS1]

Originally Posted by Dragonballful23

Here is how you solve. since 9^(x+2)=3^x, you can say 3^(2x+4)=3^x

Now, just like when you factor quadratic equations, take out the 3.
3x+4=x
2x=-4
x=-2!

You made a small mistake.
9^(x+2) = 3^x
(3^2)^(x+2) = 3^x
3^(2(x+2)) = 3^x
3^(2x+4) = 3^x
Since the base numbers are the same (3) then for the equation to be equal the exponents must be equal.
2x+4 = x
2x - x + 4 = x - x
x + 4 = 0
x + 4 - 4 = 0 - 4
x = -4
Let's check our answer.
9^(-4 + 2) = 3^(-4)
9^(-2) = 3^(-4)
1/(9^2) = 1/(3^4)
1/81 = 1/81