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anonymous

  • one year ago

Solve for x. log(x) + log(x - 3) = 1 Please explain how you got the answer.

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  1. Nnesha
    • one year ago
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    familiar with log rules ?

  2. anonymous
    • one year ago
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    No I forgot them. That's why I need help with this. Can you help me?

  3. Nnesha
    • one year ago
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    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
    • one year ago
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    so there is a plus sign which rule you should apply ?

  5. anonymous
    • one year ago
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    addition ----> multiplication

  6. anonymous
    • one year ago
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    How do you know which number is b?

  7. Nnesha
    • one year ago
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    yep so change addition to multiplication log is same so you can apply it

  8. Nnesha
    • one year ago
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    b is base

  9. Nnesha
    • one year ago
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    so log is same as log base 10 \[\huge\rm log = \log_{10}\]

  10. anonymous
    • one year ago
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    So is it log(x*(x-3))?

  11. anonymous
    • one year ago
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    Or log(x^2-3x)?

  12. Nnesha
    • one year ago
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    yep right!!

  13. anonymous
    • one year ago
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    So what do you do with the 1?

  14. Nnesha
    • one year ago
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    now you have \[\huge\rm log (x^2 -3x) =1\] next step convert log to exponential form

  15. anonymous
    • one year ago
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    How do you do that again?

  16. Nnesha
    • one year ago
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    and here is the example |dw:1438129295617:dw|

  17. Nnesha
    • one year ago
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    remember log = log base 10

  18. anonymous
    • one year ago
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    \[10^{1} = x ^{2}-3x\]

  19. anonymous
    • one year ago
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    Is that what I needed to do?

  20. Nnesha
    • one year ago
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    yep!!

  21. anonymous
    • one year ago
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    So then \[x ^{2}-3x-10\] is the next step.

  22. anonymous
    • one year ago
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    Then I have to factor right?

  23. Nnesha
    • one year ago
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    yep

  24. Nnesha
    • one year ago
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    gtg :( sorry i'm sure u know how to factor quadratic equation

  25. anonymous
    • one year ago
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    So x= -2, 5?

  26. anonymous
    • one year ago
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    Yes but I just want to verify real quick.

  27. Nnesha
    • one year ago
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    yep right

  28. anonymous
    • one year ago
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    Okay Thanks!

  29. Nnesha
    • one year ago
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    wait

  30. anonymous
    • one year ago
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    What? Did I mess up?

  31. Nnesha
    • one year ago
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    nope you are right x+2 and x-5 2 times -5 = -10 -5+2 = -3 PERFECT! SO x=-2 , x=5

  32. Nnesha
    • one year ago
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    GREAT WORK!

  33. anonymous
    • one year ago
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    Yay! Thanks again!

  34. Nnesha
    • one year ago
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    my pleasure really glad 2 help :=) smart!

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