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Math Help - 8^(2-x)=4^(3x )solve for x

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    8^(2-x)=4^(3x )solve for x

    These type of problems consistently come up on practice calculous placement tests. I always end up getting them right, but I have to plug in multiple choice answers until one works. Is there an easier way to solve this?
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    MHF Contributor Siron's Avatar
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    Re: 8^(2-x)=4^(3x )solve for x

    Yes, there's an easier way, write:
    8^{2-x}=4^{3x} as

    2^{6-3x}=2^{6x} and so:

    6-3x=6x

    ...
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    Re: 8^(2-x)=4^(3x )solve for x

    Quote Originally Posted by StudentMCCS View Post
    These type of problems consistently come up on practice calculous placement tests. I always end up getting them right, but I have to plug in multiple choice answers until one works. Is there an easier way to solve this?
    Always change to a common base if possible.
    In this case, base 2.

    In this case: 2^{6-3x}=2^{6x}
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