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anonymous

  • 5 years ago

ln(5+4x)-ln(3+x)=ln3

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  1. myininaya
    • 5 years ago
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    ln(x)-ln(y)=ln(x/y)

  2. myininaya
    • 5 years ago
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    Write ln[(5+4x)/{3+x)]=ln3

  3. myininaya
    • 5 years ago
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    base e both sides to get rid of the natural logs

  4. myininaya
    • 5 years ago
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    [(5+4x)/(3+x)]=3

  5. myininaya
    • 5 years ago
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    Solve for x

  6. myininaya
    • 5 years ago
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    5+4x=3(3+x) I multiply 3+x on both sides

  7. myininaya
    • 5 years ago
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    5+4x=9+3x Distributive property

  8. myininaya
    • 5 years ago
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    5+x=9 so x=9-5=4

  9. myininaya
    • 5 years ago
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    Always check your solution when working with log. You never know the solution may not be in the domain

  10. anonymous
    • 5 years ago
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    thank you for your help

  11. myininaya
    • 5 years ago
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    In this case it is, because 5+4x and 3+x is positive for x=4

  12. myininaya
    • 5 years ago
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    no problem

  13. anonymous
    • 5 years ago
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    I have one more question. Is that ok?

  14. myininaya
    • 5 years ago
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    Go ahead

  15. anonymous
    • 5 years ago
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    r=p-k ln t, for t

  16. myininaya
    • 5 years ago
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    So we want to solve for t. First get the ln(t) by itself

  17. myininaya
    • 5 years ago
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    Subtract p on both sides: r-p=-klnt

  18. myininaya
    • 5 years ago
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    Now divide -k on both sides: (r-p)/(-k)=lnt

  19. myininaya
    • 5 years ago
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    Base e both sides to get ride of the natural log

  20. myininaya
    • 5 years ago
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    e^[-(r-p)/k]=t

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