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Math Help - Log simplification.

  1. #1
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    Log simplification.

    1. logx + log sqroot x^3 - 2log x
    ANS: 1/2log

    2. log x/(sqroot x) + log sq.root x^5 - 7/3 log x
    ANS: 2/3log

    3. 2log2x - log 4y - log sqroot (xy)
    ANS: x^(3/2) y^(-3/2)

    how do i do these?, you dont have to answer them fully, since i would like to learn or if you show all steps so i can learn.

    Can someone guide me through these?
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  2. #2
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    Re: Log simplification.

    Hey skg94.

    For these recall that log(xy) = log(x) + log(y) and that log(x/y) = log(x) - log(y).

    In terms of your answers are you looking for terms in terms of log(x) (You write log but is it instead log(x))?
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  3. #3
    MHF Contributor MarkFL's Avatar
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    Re: Log simplification.

    To simplify these expressions, you need to know a few properties of logs and concerting from radical notation to rational exponent notation.

    \log_a(x)+\log_a(y)=\log_a(xy)

    \log_a(x)-\log_a(y)=\log_a\left(\frac{x}{y} \right)

    \log_a(b^c)=c\cdot\log_a(b)

    \sqrt[n]{x^m}=x^{\frac{m}{n}}

    The answers you have supplied are incomplete, although I can tell what is intended.

    Using the above properties, see if you can get the desired result. If you get stuck, post your working and state where you are stuck.
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  4. #4
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    Re: Log simplification.

    Well they are the answers in my textbook i cant really do much about them, since im pretty sure my teachers look for the same, maybe not.

    if they are incomplete what are the correct answers?

    x* x^1.5 / x^2

    x^2.5/x^2
    2.5-2 = x^.5

    so is that why its 1/2 log x? suppose i got that one at least.

    2. x*x^2.5/x^1/2 * x^(7/3) =x^3.5/ x^ 17/6 = x^ 2/3

    2/3 log x

    3. 4x^2 / 4y * x^1/2 * y^1/2
    4x^2/ 4y^1.5 * x^1/2

    x^1.5 y^1.5 -- hm not negative 1.5?


    well i got it now if you see any errors let me know
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  5. #5
    MHF Contributor MarkFL's Avatar
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    Re: Log simplification.

    The first two answer provided by the book do not contain an argument for the log function, which is meaningless. The last one does not include the log function, but just the argument. It certainly is not the way the answers should be given.

    If I were working these problems, this is the way I would show my work for the first one:

    1.) \log(x)+\log(\sqrt{x^3})-2\log(x)

    \log(x)+\log({x^{\frac{3}{2}}})-\log(x^2)

    \log\left(\frac{x\cdot x^{\frac{3}{2}}}{x^2} \right)

    \log(x^{\frac{1}{2}})

    \frac{1}{2}\log(x)
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  6. #6
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    Re: Log simplification.

    yes it was just my laziness it does have the x and such in the textbook my apologies.
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