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Math Help - log problem..is that correct my answer??

  1. #1
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    log problem..is that correct my answer??

    Given log_3{7}=1.771 and  log _3{5}=1.465.find

    a) log_9{35}

    this is my step:
    =log{_\sqrt{9}}35^\frac{1}{2}

    =\frac{1}{2}log_3(5)(7)

    =\frac{1}{2}log_3{5}+log_3{7}

    =\frac{1}{2}(1.465)+(1.771)

    =2.5035
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  2. #2
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    I do not think your answer is correct. I imagine you're supposed to use the properties of logarithms to combine the given information in such a way that you can compute the required logarithm. Note that the bases are different. What do you suppose you have to do there?
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  3. #3
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    what should i do?
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  4. #4
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    Well, you're given \log_{3}(7) and \log_{3}(5). You're after the quantity \log_{9}(35). What you'd like to do is have the bases multiply, and the arguments multiply. If you look at this page, does it give you any ideas on how to do that?
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  5. #5
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    Quote Originally Posted by mastermin346 View Post
    Given log_3{7}=1.771 and  log _3{5}=1.465.find

    a) log_9{35}

    this is my step:
    =log{_\sqrt{9}}35^\frac{1}{2}

    =\frac{1}{2}log_3(5)(7)

    =\frac{1}{2}log_3{5}+log_3{7}

    =\frac{1}{2}(1.465)+(1.771)

    =2.5035
    All your considerations and calculations are OK. There is only a pair of brackets missing:

    =\frac{1}{2}\left((1.465)+(1.771)\right)
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  6. #6
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    Hang on. Just saw something in the OP. Try re-computing the last number from the second-to-last line. That's an average. Your answer at the end is clearly wrong, but I think the steps up to that point are correct.

    [EDIT] Earboth sees the problem correctly.
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