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Math Help - Find in terms of a and c for logs

  1. #1
    Member smmmc's Avatar
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    Find in terms of a and c for logs

    Hey

    I dont understand what the question is asking, do i sub the fraction into the log10(x)=a, the x part... ?
    above attached


    thanks alot
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  2. #2
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    Hi smmmc!

    Quote Originally Posted by smmmc View Post
    Hey

    I dont understand what the question is asking, do i sub the fraction into the log10(x)=a, the x part... ?
    above attached


    thanks alot
    You have to use the logarithm-rules, i.e.

    log(a/b) = log(a) - log(b)

    and log(a*b) = log(a)+log(b)

    and log(a^n) = n*log(a)

    Now lets see.

    log(\frac{100x^3y^{-1/2}}{y^2})

    Just using the rules leads to

    log(100x^3y^{-1/2})-log(y^2)

    log(100x^3y^{-1/2})-2log(y)

    log(100)+log(x^3)+log(y^{-1/2})-2log(y)

    log(100)+3log(x)-1/2*log(y) - 2log(y)

    Do you see which rule I used in each step? Did you understand everything?

    log_{10}(100) = ... well, you know how to calculate it, right?

    Regards
    Rapha
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  3. #3
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    You are being asked to apply the rules:

    \log_b \frac{x}{y} = \log_b x - \log_b y,

    \log_b xy = \log_b x + \log_b y,

    and \log_b x^k = k\log_b x.

    Apply these rules to the given expression, make the substitutions they give you, and simplify where necessary.

    EDIT: Too slow!
    Last edited by AlephZero; July 18th 2009 at 08:14 PM. Reason: EDIT: Too slow!
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by smmmc View Post
    Hey

    I dont understand what the question is asking, do i sub the fraction into the log10(x)=a, the x part... ?
    above attached


    thanks alot

    =(\log_{10}100x^3y^{1/2})-(\log_{10}y^2)=[(\log_{10}100)+(\log_{10}x^3)+(\log_{10}y^{-1/2})]+\log_{10}y^2

    Bring down all the exponents and........ can you substitute and simplify?
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  5. #5
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    I would first rewrite the fraction as a sum/difference of logs:
    \log_{10} \left(\frac{100x^3 y^{-1/2}}{y^2}\right)
    \begin{aligned}<br />
&= \log_{10} \left(\frac{100x^3}{y^{5/2}}\right) \\<br />
&= \log_{10} (100) + \log_{10} (x^3) - \log_{10} (y^{5/2})<br />
\end{aligned}
    Can you take it from here?


    01


    EDIT: Ack, beaten to it by three posters!
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  6. #6
    Member smmmc's Avatar
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    Hey thank you all ! Thanks for providing me hints and directing me to the right way
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