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Math Help - [SOLVED] Log equation help,

  1. #1
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    [SOLVED] Log equation help,

    When solving an equation involving logs, I've gotten this far

    4 = Log5x/log625x

    four is equal to log (base 5) x over log (base 625) x

    I know x is equal to 25. But how do I get to that answer not using guess and check?
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  2. #2
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    Quote Originally Posted by jsmith90210 View Post
    When solving an equation involving logs, I've gotten this far

    4 = Log5x/log625x

    four is equal to log (base 5) x over log (base 625) x

    I know x is equal to 25. But how do I get to that answer not using guess and check?
    First,U should know Log 625 X= (log 5 x)/(log 5 625) ,So U can solve it.
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  3. #3
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    Quote Originally Posted by jsmith90210 View Post
    [SIZE=2]four is equal to log (base 5) x over log (base 625) x
    Since 625 = 5^4, then the change-of-base formula can prove helpful:

    . . . . . \log_{625}(x)\, =\, \frac{\log_5(x)}{\log_5(625)}\,=\,\frac{\log_5(x)}  {\log_5(5^4)}

    Then apply a log rule and the definition of logs to convert \log_5(5^4) to just "4".

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  4. #4
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    Excuse my ignorance

    Excuse my ignorance, but how does that help me.

    Of course



    which would leave:

    (Log(base 5) x) OVER (log(base 5) x / 4) on one side

    and 4 on the other side

    of course 4 = 4
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  5. #5
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    Solved

    Nevermind, I should have seen this. The answer is actually

    x = 5^n, where n > 1
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