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    solve exponential equation using logs...

    solve exponential equation using logs:

    (4^x) * (5^x) = 6^x
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    Quote Originally Posted by GreenTea1mochi View Post
    solve exponential equation using logs:

    (4^x) * (5^x) = 6^x
    $\displaystyle 4^x \cdot 5^x = 6^x$

    $\displaystyle (4 \cdot 5)^x = 6^x$

    $\displaystyle 20^x = 6^x$

    $\displaystyle x\log(20) = x\log(6)$

    $\displaystyle x\log(20) - x\log(6) = 0$

    $\displaystyle x[\log(20) - \log(6)] = 0$

    $\displaystyle x = 0$
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  3. #3
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    Quote Originally Posted by GreenTea1mochi View Post
    solve exponential equation using logs:

    (4^x) * (5^x) = 6^x
    A different method

    $\displaystyle log(4^x 5^x) = x\,log(6)$

    $\displaystyle x\,log(4)+x\,log(5) = x\,log(6)$

    $\displaystyle x(log(4)+log(5)-log(6))=0$

    $\displaystyle x = 0$
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