anonymous 4 years ago Okay I'm almost there but the answer I'm getting is incorrect.

1. anonymous

$\ln (x)+\ln (x-2)=\ln 8$

2. anonymous

then...$\ln (x)(x-2)=\ln 8$

3. anonymous

then...$\ln (x ^{2}-2x)=\ln 8$

4. anonymous

then drop the ln... $x^{2}-2x=8$

5. anonymous

going good...

6. anonymous

well you e^ both sides. That's how the ln cancel. But then you are left with a quadratic equation

7. anonymous

split the two, $x^{2}=8$ and $-2x=8$

8. anonymous

thats incorrect

9. anonymous

true ok ok

10. anonymous

11. anonymous

yup

12. anonymous

Compare your quadratic equation with $$ax^2+bx+c=0$$ find a,b,c then the two roots of x are: $$\huge{x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}}$$

13. anonymous

x^2-2x-8=0

14. anonymous

okay gimme a second to work that out.

15. anonymous

sure.

16. anonymous

*** and need to remember to check for valid values of x. if you are taking ln(x) and ln(x-2) what can't x be?

17. anonymous

You can always complete the square. That's another way of solving this without the long work of using the quadratic

18. anonymous

2

19. anonymous

whats finishing the square? Sounds like a shortcut I was denied...

20. anonymous

granted

21. anonymous

shortcut only if u have some prsctice.... u wanna learn that ?

22. anonymous

... or just factor? $x^2-2x-8=0=(x-?)(x+?)$

23. anonymous

practice some more then use that form

24. anonymous

factoring is best here..

25. anonymous

can u factor ?

26. anonymous

I'll give it a shot! :)

27. anonymous

sure do :)

28. anonymous

go han!!!! go ku!!!! dominate the problem TEAMWORKKKK

29. anonymous

? jerry ?

30. anonymous

GO HAN GO KU

31. anonymous

$x^2−2x−8=0=(x−A)(x+B)\\ A*B=-8\\ A+B=-2$ Find A and B

32. anonymous

Almost there....

33. anonymous

You have a system of question where you can simply plug in one equation to another if you can't see it right away. Then solve for the missing variable.

34. anonymous

its (x-4)(x+2)

35. anonymous

thats correct :)

36. anonymous

so what are 2 values of x u got ?

37. anonymous

ten solving its 4 and -2

38. anonymous

$(x-4)(x+2)=0$

39. anonymous

and -2 would be extraneous

40. anonymous

but can x be -2 ?? think ....

41. anonymous

yes, so x is only = ?

42. anonymous

4?

43. anonymous

yup, u got it :)

44. anonymous

HAZUAHH!

45. anonymous

THanks everyone! I really appreciate it! :)

46. anonymous

welcome ^_^