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Homework Help: How do you solve for x in this radical equation?

  1. Oct 23, 2005 #1
    sqrt[x]{64} = 4

    How do you solve for x?

    I mean obviously the answer is x = 3 but how do you prove this algebraically?
     
    Last edited: Oct 24, 2005
  2. jcsd
  3. Oct 24, 2005 #2

    TD

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    Homework Helper

    You can use logarithms or 'play' with powers:

    [tex]\sqrt[x]{{64}} = 4 \Leftrightarrow 64^{1/x} = 4 \Leftrightarrow \left( {4^3 } \right)^{1/x} = 4 \Leftrightarrow 4^{3/x} = 4^1 \Leftrightarrow \frac{3}
    {x} = 1[/tex]
     
  4. Oct 24, 2005 #3

    HallsofIvy

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    I really, really wish people would say "x-root" rather than "x-square root" or root[x} instead of (as here) sqrt[x]. "square root" means specifically
    [tex]^2\sqrt{x}[/tex]
     
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