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Math Help - Logarithms

  1. #1
    Member rtblue's Avatar
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    Logarithms

    Hello everyone, I had a question about a problem involving some logs:

    5log_32+2log_910=?

    I'm not quite sure where to start with this problem, any suggestions would be appreciated.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by rtblue View Post
    Hello everyone, I had a question about a problem involving some logs:

    5log_32+2log_910=?

    I'm not quite sure where to start with this problem, any suggestions would be appreciated.
    A good place to start might be to use the change of base formula
    Logarithm - Wikipedia, the free encyclopedia

    \log_9(a)=\frac{\log_{3}(a)}{\log_3(9)}=...

    You will need to use other log properties as well.
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  3. #3
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    Hint: 2\log_9(10)=\log_3(10).
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  4. #4
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    That's because y= log_9(x) is the same as x= 9^y= (3^2)^y= 3^{2y} so that log_3(x)= 2y= 2log_9(x).
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  5. #5
    Super Member bigwave's Avatar
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    use ln

    using as has been mentioned you could too rewrite to:

    \log_3{32} + \log_9{100}

    then

    \frac{ln32}{ln3} + \frac{ln100}{ln9}<br /> <br />
\Rightarrow<br /> <br />
3.15 + 4.19 = 5.25(approx)
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