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Math Help - Exponents.

  1. #1
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    Exponents.

    Solve for :




    I know 9 is 3^2 and 4 is 2^2

    but how can i simplify this while knowing the above?
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Exponents.

    To make it easy you can take the \log of both sides and use \log(a^b)=b\log(a) and you can also use a^{x+y}=a^{x}\cdot a^{y} in the first place
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  3. #3
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    Re: Exponents.

    so would it be


    9x/3 log 9 = 8x/2 log 4 ?
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Exponents.

    If you use the rule I suggested then you get:
    9^{9x-3}=4^{8x-2}
    \Leftrightarrow \log(9^{9x-3})=\log(4^{8x-2})
    \Leftrightarrow (9x-3)\log(9)=(8x-2)\log(4)
    \Leftrightarrow 9x\log(9)-3\log(9)=8x\log(4)-2\log(4)
    \Leftrightarrow 9x\log(9)-8x\log(4)=3\log(9)-2\log(4)
    \Leftrightarrow x[9\log(9)-8\log(4)]=3\log(9)-2\log(4)
    \Leftrightarrow ...
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  5. #5
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    Re: Exponents.

    ohh!!! ah oki i gotcha now
    all the rules of exponents just confuse me!

    thanks so much! do you mind taking a look at my half life problem i posted earlier?
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Exponents.

    You're welcome!

    To solve exponential equations then you really have to know this basic rules.
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