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Math Help - Logarithmic problem

  1. #1
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    Logarithmic problem

    Hi,

    Can someone please tell me how to solve the attached logarithmic problem ? the answer should be 5.
    Attached is also my working.

    Thanks
    Attached Thumbnails Attached Thumbnails Logarithmic problem-capture.png   Logarithmic problem-capture1.png  
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  2. #2
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    Re: Logarithmic problem

    log(x^2-5)-log(x) = log(4)

    Use the logarithmic law that states that log(a)-log(b) = log(a/b)


    log((x^2-5)/x) = log(4) (Here's were your error is in your calculation)
    (x^2-5)/x = 4
    x^2-5 = 4x

    Solving this equation gives the solution x = -1 and x = 5.

    But since negative solutions are not defined in the equation log(x) the only solution is x = 5.
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  3. #3
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    Re: Logarithmic problem

    the original equation was ...

    \log\left(\frac{x^2-5}{x}\right) = \log{4}

    not ...

    \log(x^2-5) - \log{x} = \log{4}



    why can't x = -1 ?
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    Re: Logarithmic problem

    Thanks for the reply. At skeeter, no the first one was the is the original equation. There is another attachment.

    Another problem. The result of the attached problem is 6.66 while on the book it states that the result should be 6.058. What am I doing wrong? Isn't it gust (Ln14.91/(Ln1.5) ??
    Attached Thumbnails Attached Thumbnails Logarithmic problem-capture.png  
    Last edited by aritech; November 11th 2012 at 12:55 PM.
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  5. #5
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    Re: Logarithmic problem

    Quote Originally Posted by aritech View Post
    Thanks for the reply. At skeeter, no the first one was the is the original equation. There is another attachment.

    Another problem. The result of the attached problem is 6.66 while on the book it states that the result should be 6.058. What am I doing wrong? Isn't it gust (Ln14.91/(Ln1.5) ??
    i would just take ^1/1.5 on both side on that problem :P
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  6. #6
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    Re: Logarithmic problem

    Quote Originally Posted by aritech View Post
    Thanks for the reply. At skeeter, no the first one was the is the original equation. There is another attachment.
    ok ... now I see it.
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  7. #7
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    Re: Logarithmic problem

    Hi,

    Can someone tell me how to work the binomial attached??

    the answer should be 34749 p^8q^5
    Attached Thumbnails Attached Thumbnails Logarithmic problem-181120121252.jpg  
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  8. #8
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    Re: Logarithmic problem

    your binomial coefficient is incomplete ...

    \binom{13}{8} \cdot (3p)^8 \left(\frac{q}{3}\right)^5

    \frac{13!}{8!(13-8)!} \cdot (3^3 p^8 q^5)

    34749p^8q^5

    ... next time, start a new problem with a new post. Do not piggy-back onto an older one.
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  9. #9
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    Re: Logarithmic problem

    From where did you bring the 13/8 ??

    Attached is the full question and working:
    Attached Thumbnails Attached Thumbnails Logarithmic problem-181120121253.jpg  
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  10. #10
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    Re: Logarithmic problem

    Quote Originally Posted by aritech View Post
    From where did you bring the 13/8 ??

    Attached is the full question and working:
    Where are your binomial coefficients?

    you need to review the general binomial expansion ...

    Thanks from aritech
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