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Math Help - Find Values Log

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    Find Values Log

    There exist positive intergers A,B,C with no common factor greater than 1, such that Alogbase200(5) + Blogbase200(2)=C, find A,B,C
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    Quote Originally Posted by KingV15 View Post
    There exist positive intergers A,B,C with no common factor greater than 1, such that Alogbase200(5) + Blogbase200(2)=C, find A,B,C
    1. Use the base 200 with your equation:

    A\log_{200}(5) + B\log_{200}(2)=C

    5^A \cdot 2^B = 200^C

    5^A \cdot 2^B = (5^2 \cdot 2^3)^C

    Therefore:

    A = 2C~\wedge~B=3C

    Choose a number for C.
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