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Math Help - Logs

  1. #1
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    Logs

    Given that logbase6(2)=0.387, determine the value of logbase6(9)
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  2. #2
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    Quote Originally Posted by Tiger View Post
    Given that logbase6(2)=0.387, determine the value of logbase6(9)
    \log_{6} (9) = \log_{6} (\frac{18}{2}) = \log_{6} (\frac{ (6)(3) }{ (2) })
    =\log_{6} (6) + \log_{6} (3) - \log_{6} (2)
    =\log_{6} (6) + \log_{6} (\frac{6}{2}) - \log_{6} (2)
    =\log_{6} (6) + \log_{6} (6) - \log_{6} (2) - \log_{6} (2)
    =1 + 1 - 2 \log_{6} (2)
    =2 - 2 (0.387)
    =2 - 0.774
    =1.226
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  3. #3
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    Hello, Tiger!

    A slight variation of the General's solution . . .


    Given: . \log_6(2)\,=\,0.387,\:\text{ determine the value of: }\:\log_6(9)

    \log_6(9) \;\;=\;\;\log_6\left(\frac{36}{4}\right) \;\;=\;\;\log_6(36) - \log_6(4) \;\;=\;\;\log_6\left(6^2\right) - \log_6\left(2^2\right)

    . . =\;\;2\underbrace{\log_6(6)}_{\text{This is 1}} - 2\log_6(2) \;\;=\;\; 2 - 2\log_6(2) \;\;=\; \;2 - 2(0.387) \;\;=\;\;1.226

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  4. #4
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    logs

    originally postedby Tiger
    given logbase6(2)=.387 find logbase6(9)

    Gents
    Another slight variation

    logbase6(9)=2xlog base6(6/2) Result is the same

    bjh
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