## anonymous 5 years ago solve the equation. Separate by commas, if more than one answer. x^(2)9^(x)-2x9^(x)=3(9^(x))

1. anonymous

$x ^{2}9^{x}-2x9^{x}=3(9^{x})$

2. anonymous

Do this...

3. anonymous

Bring over the right-hand side and take out the common factor of 9^x. You have$9^x(x^2-2x-3)=0$

4. anonymous

That means

5. anonymous

either $9^x=0$or$x^2-2x-3=0$

6. anonymous

There is no x here that will make 9^x zero (if you plot any exponential function, you'll see that it never crosses below the x-axis)

7. anonymous

Thanks a lot for explaining the steps, much appreciated.

8. anonymous

But,$x^2-2x-3=(x+1)(x-3)$so your second factor has that$(x+1)(x-3)=0 \rightarrow x=-1,3$

9. anonymous

No worries.

10. anonymous

feel free to become a fan ;)

11. anonymous

I will! :)

12. anonymous

how do I become a fan though?

13. anonymous

There should be a blue link next to my name...says, "Become a fan"

14. anonymous

nice, very nice