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Math Help - 6^x=4

  1. #1
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    6^x=4

    6^x=4 ? i have a sudden black out and i can't remember the rule for when solving equations like this one.. to complicate things i'm not allowed to answer with x=log4/log6
    Last edited by weasley74; February 11th 2008 at 12:25 PM.
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  2. #2
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    when two logs are divided they can be written thus:

    x= log(4/6)

    same as

    x= log4 - log6
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  3. #3
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    and what about if log isn't allowed to be in the answer at all?
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  4. #4
    Senior Member topher0805's Avatar
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    Are you familiar with the change of base formula?
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  5. #5
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    I don't think so.. it's possible that I am, just that it has a very different name in Swedish.. ^^
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  6. #6
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    enter it into a calculator you could also write it as x=log (base 4) *6

    could you tell me the question in full?
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  7. #7
    Senior Member topher0805's Avatar
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    Are you not allowed to use a calculator? If you are then you can find the exact value.
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  8. #8
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    here's the kicker.. i'm not allowed to use a calculator ^^ yay (not so much)

    ^6 log4..
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  9. #9
    Super Member angel.white's Avatar
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    Quote Originally Posted by weasley74 View Post
    6^x=4 ? i have a sudden black out and i can't remember the rule for when solving equations like this one.. to complicate things i'm not allowed to answer with x=log4/log6
    Method1:
    Initial equation
    6^x=4

    Take the log of both sides (it doesn't matter what base you use)
    log(6^x)=log(4)

    One of the properties of logs is that if they are the log of a number to a power, they are the same as the power times the log of the number. Meaning log(6^x)=xlog(6) so
    xlog(6)=log(4)

    Divide both sides by log(6)
    x=\frac {log(4)}{log(6)}


    Method2
    Initial equation
    6^x=4

    Take log base 6 of both sides
    log_6(6^x) = log_6(4)

    Simlify
    x = log_6(4)

    Use change of base formula to rewrite in a format you can plug into a calculator. Change of base formula says log_a(b) = \frac{log_c(b)}{log_c(a)} This works for any value of c. Typically the value chosen is 10 or e, as log base ten and log base e (natural log) are the two most common logs, and are programmed into any decent calculator.
    x = \frac{log(4)}{log(6)}
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  10. #10
    Super Member angel.white's Avatar
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    Quote Originally Posted by topher0805 View Post
    Are you not allowed to use a calculator? If you are then you can find the exact value.
    x=\frac{log(4)}{log(6)}
    is the exact value. A decimal value is not exact, it is an approximation, because it cannot get to every digit in the decimal place (if the value is irrational).
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  11. #11
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    I thought the poster said you can't answer with log
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  12. #12
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    Quote Originally Posted by OzzMan View Post
    I thought the poster said you can't answer with log
    correct.
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  13. #13
    Super Member angel.white's Avatar
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    Quote Originally Posted by OzzMan View Post
    I thought the poster said you can't answer with log
    Then the answer he is looking for is
    x = \frac{log(4)}{log(6)} \approx 0.77370561446908317374049227693595

    Which is not exact, and I would seem to require a calculator to find.

    It seems most likely to me that they are looking for x=\frac{log(4)}{log(6)} or x=log_6(4) as these values are exact, and one of the other requirements was that he could not use a calculator.
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  14. #14
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    What math class is this for? The only way i know how to answer this problem is with logarithms lol. This is interesting.
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  15. #15
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    There must be another way to do this without logarithms.
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