## anonymous one year ago Solve for x. log(x) + log(x - 3) = 1 Please explain how you got the answer.

1. Nnesha

familiar with log rules ?

2. anonymous

No I forgot them. That's why I need help with this. Can you help me?

3. Nnesha

quotient rule$\large\rm log_b y - \log_b x = \log_b \frac{ x }{ y}$ to condense you can change subtraction to division product rule $\large\rm log_b x + \log_b y = \log_b( x \times y )$ addition ----> multiplication power rule $\large\rm log_b x^y = y \log_b x$

4. Nnesha

so there is a plus sign which rule you should apply ?

5. anonymous

6. anonymous

How do you know which number is b?

7. Nnesha

yep so change addition to multiplication log is same so you can apply it

8. Nnesha

b is base

9. Nnesha

so log is same as log base 10 $\huge\rm log = \log_{10}$

10. anonymous

So is it log(x*(x-3))?

11. anonymous

Or log(x^2-3x)?

12. Nnesha

yep right!!

13. anonymous

So what do you do with the 1?

14. Nnesha

now you have $\huge\rm log (x^2 -3x) =1$ next step convert log to exponential form

15. anonymous

How do you do that again?

16. Nnesha

and here is the example |dw:1438129295617:dw|

17. Nnesha

remember log = log base 10

18. anonymous

$10^{1} = x ^{2}-3x$

19. anonymous

Is that what I needed to do?

20. Nnesha

yep!!

21. anonymous

So then $x ^{2}-3x-10$ is the next step.

22. anonymous

Then I have to factor right?

23. Nnesha

yep

24. Nnesha

gtg :( sorry i'm sure u know how to factor quadratic equation

25. anonymous

So x= -2, 5?

26. anonymous

Yes but I just want to verify real quick.

27. Nnesha

yep right

28. anonymous

Okay Thanks!

29. Nnesha

wait

30. anonymous

What? Did I mess up?

31. Nnesha

nope you are right x+2 and x-5 2 times -5 = -10 -5+2 = -3 PERFECT! SO x=-2 , x=5

32. Nnesha

GREAT WORK!

33. anonymous

Yay! Thanks again!

34. Nnesha

my pleasure really glad 2 help :=) smart!

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