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Math Help - logarithm help

  1. #1
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    logarithm help

    1.express in terms of log a, log b.

    \log \frac{1}{ab^4}

    2.express as a single logarithm.

    \frac{1}{2}\log 80 - \frac{1}{2}\log 5

    thanks
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  2. #2
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    Quote Originally Posted by llkkjj24 View Post
    1.express in terms of log a, log b.

    \log \frac{1}{ab^4}

    2.express as a single logarithm.

    \frac{1}{2}\log 80 - \frac{1}{2}\log 5

    thanks
    Use these two facts:

    log(x\cdot y) = log(x) + log(y)

    log(\frac{x}{y}) = log(x) - log(y)

    And for the second, note that \frac{1}{2}log(80) - \frac{1}{2}log(5) = \frac{1}{2}(log(80)-log(5)).

    Can you do it now?
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  3. #3
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    ye, i did it before, but my answer didn't match of the book.
    so was hoping for someone to work it out so i can see my mistakes
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  4. #4
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    Quote Originally Posted by llkkjj24 View Post
    so was hoping for someone to work it out so i can see my mistakes
    Post your work so we can see your mistakes, it will be easier to assist you this way.
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  5. #5
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    for 1 i had trouble of how to manipulate the fraction \frac{1}{ab^4}.
    is this the correct form? \log a - \log b ^ -4

    for 2 i did using the laws of logs.

    \log 80^\frac{1}{2} - \log 5^\frac{1}{2}

    then \log \frac{\log \sqrt{80}}{\log \sqrt{5}}
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  6. #6
    Senior Member Stroodle's Avatar
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    Using the properties posted above by Defunkt, you get:

    log\left ( \frac{1}{ab^4}\right )

    \Rightarrow log(1)-\left[log(a)+log(b^4)\right]

    \Rightarrow 0-log(a)-4log(b)

    \Rightarrow -log(a)-4log(b)

    and for the second one:

    \frac{1}{2}log(80)-\frac{1}{2}log(5)

    \Rightarrow \frac{1}{2}\left[log(80)-log(5)\right]

    \Rightarrow\frac{1}{2}log(\frac{80}{5})

    \Rightarrow\frac{1}{2}log(16)

    \Rightarrow\log(16^\frac{1}{2})

    \Rightarrow\log(4)
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  7. #7
    Senior Member Stroodle's Avatar
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    Quote Originally Posted by llkkjj24 View Post
    for 1 i had trouble of how to manipulate the fraction \frac{1}{ab^4}.
    is this the correct form? \log a - \log b ^ -4

    for 2 i did using the laws of logs.

    \log 80^\frac{1}{2} - \log 5^\frac{1}{2}

    then \log \frac{\log \sqrt{80}}{\log \sqrt{5}}
    You can also solve the second problem this way:

    \frac{1}{2}log(80)-\frac{1}{2}log(5)

    \Rightarrow log\left ( \frac{\sqrt{80}}{\sqrt{5}}\right )

    \Rightarrow log(4)

    (after rationalising and simplifying the fraction)
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  8. #8
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    thanks , problem solved
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