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Math Help - exponential base. logarithm.

  1. #1
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    exponential base. logarithm.

    so working on a few exponential functions. i know that you can make the exponents equal to one another if the bases are the same but what if there is a single variable and the terms are multiplied/added.

    what i have so far:

    3^{2x}-2*3^{x+5}+3^{10} = 0
    (3^{2x})(3^{x+5})+3^{10} = 2

    is it correct to move over the 2 to work with the same bases easier?
    or is this completely off and i should use logarithm and natural log? if so, please give hints as to how to work it out.


    thankyou~
    Last edited by ninjuhtime; November 30th 2008 at 09:16 PM.
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  2. #2
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    Hello, ninjuhtime!

    What i have so far:

    3^{2x}-2\cdot3^{x+5}+3^{10} \:= \:0

    (3^{2x})(3^{x+5})+3^{10} = 2 . . . . Definitely illegal!
    It's hard to see it, but the expression is a perfect square . . .

    We have: . \left(3^x - 3^5\right)^2 \:=\:0 \quad\Rightarrow\quad 3^x - 3^5 \:=\:0 \quad\Rightarrow\quad 3^x \:=\:3^5 \quad\Rightarrow\quad\boxed{ x \:=\:5}

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  3. #3
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    thankyou! i guess i oversaw what it was since long problems are usually intimidating.
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