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Math Help - Logarithmic function question

  1. #1
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    Logarithmic function question

    Hi guys I am back,

    So I'm doing logarithmic function exercises in textbook and need to evaluate some. This one is:

    log(base)8 .25

    My answer book shows the answer as: log(base)8 8^-2/3 = -2/3

    I understand this but would like to understand the easiest procedure to go from .25 to its equivalent 8^-2/3

    Thanks

    Edit: my usual way is to write out the exp form like: 8^x = 1/4, but then I get stuck ha
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  2. #2
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    Quote Originally Posted by DannyMath View Post

    Edit: my usual way is to write out the exp form like: 8^x = 1/4, but then I get stuck ha
    then get "unstuck" ...

    8^x = \frac{1}{4}

    (2^3)^x = \frac{1}{2^2}

    2^{3x} = 2^{-2}

    3x = -2

    x = -\frac{2}{3}
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  3. #3
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    See that's what I needed, I keep learning these little things along the way and understanding more and more. It's not like I'm asking for answers I hope. HAHA

    Thank you!
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  4. #4
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    It comes down to asking yourself

    8 and 4 are powers of what number?
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  5. #5
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    Yes that is much clearer to me now. Thank you!
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