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Math Help - Solve without using log

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    Solve without using log

    solve \frac{3^n}{49}=1029^n without using logarithms
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  2. #2
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    \frac{3^n}{49} = 1029^n

    \frac{3^n}{1029^n} = 49

    \left(\frac{3}{1029}\right)^n = 49

    \left(\frac{1}{343}\right)^n = 49

    \frac{1^n}{343^n} = 7^2

    \frac{1}{(7^{3})^n} = 7^2

    \frac{1}{7^{3n}} = 7^2

    7^{-3n} = 7^2

    -3n = 2

    n = -\frac{2}{3}.
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  3. #3
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    Quote Originally Posted by Punch View Post
    solve \frac{3^n}{49}=1029^n without using logarithms
    Hint: 1029 = 3*7*7*7. Rewrite RHS in a way that allows you to cancel something out.

    Edit: Too slow, so might as well show all the steps I had in mind.

    \frac{3^n}{49}=1029^n

    3^n7^{-2}=3^n7^{3n}

    7^{-2}=7^{3n}

    -2=3n

    n=-\frac{2}{3}
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