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Math Help - Find value of n

  1. #1
    Senior Member Mukilab's Avatar
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    Find value of n

    No calculator, method not answer please

    3\cdot \sqrt{27}=3^{n}
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  2. #2
    Senior Member Dinkydoe's Avatar
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    Divide both sides by 3 to obtain: \sqrt{27} = 3^{n-1}

    Now take the square of both sides to get:  27 = 3^{2(n-1)}

    We know that 27 = 3^3 = 3^{2(n-1)} so 3 = 2(n-1).

    This gives:  5 = 2n so \frac{5}{2} = n
    (you can ofcourse save some steps: 3\cdot \sqrt{27} = 3\cdot \sqrt{3^3} = 3^{\frac{3}{2}+1} = 3^{\frac{5}{2}} \rightarrow n = \frac{5}{2})
    Last edited by Dinkydoe; January 7th 2010 at 10:20 AM.
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  3. #3
    Senior Member Mukilab's Avatar
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    Quote Originally Posted by Dinkydoe View Post
    Divide both sides by 3 to obtain: \sqrt{27} = 3^{n-1}

    Now take the square of both sides to get:  27 = 3^{2(n-1)}

    We know that 27 = 3^3 = 3^{2(n-1)} so 3 = 2(n-1).

    This gives:  5 = 2n so \frac{5}{2} = n
    (you can ofcourse save some steps: 3\cdot \sqrt{27} = 3\cdot \sqrt{3^3} = 3^{\frac{3}{2}+1} = 3^{\frac{5}{2}} \rightarrow n = \frac{5}{2})
    How did you get 3=2(n-1) from 3^{2(n-1)}??/
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  4. #4
    Senior Member Dinkydoe's Avatar
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    if 3^3 = 3^{2(n+1)} this means that 3 = 2(n+1)

    Since  a^b = a^c \rightarrow b = c
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  5. #5
    Senior Member Mukilab's Avatar
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    Thanks for the formula I can add to my list!
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