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Boolean
Boolean asked in Science & MathematicsMathematics · 9 years ago

Solving for the nth power?

I was wondering how to solve for the nth power (ex. n√16,807 = 7). the one way I know how to solve the this currently is a trial and error method, and I'm really looking for a more efficient way of evaluating the problem. Thanks

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  • M3
    Lv 7
    9 years ago
    Favorite Answer

    take logs

    (1/n)*log 16807 = log 7,

    n = log 16807 /log 7 = 5 <------

  • Anonymous
    9 years ago

    I take it you mean the n-th root in your example. Otherwise there is no "n-th power". Or, better, 1/n power.

    If so, learn how to write properly as it points to the solution: (16,807)^(1/n) = 7. Take the log of both side to get rid of the exponent => (1/n) ln(16,807) = ln 7 => n = (ln 16,807)/ln 7, which turns out to be n = 5.

    7^5 = 16,807

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