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Thread: Radical Equations

  1. #1
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    Radical Equations

    I found the following question in my Math B book.
    It is a radical equation problem. I played with this question for 20 minutes and got nowhere.

    Here it is:

    8x^(-3/4) = 27

    Solve for x.

    The answer is x = 16/81. How do I get this answer?
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  2. #2
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    Quote Originally Posted by magentarita View Post
    I found the following question in my Math B book.
    It is a radical equation problem. I played with this question for 20 minutes and got nowhere.

    Here it is:

    8x^(-3/4) = 27

    Solve for x.

    The answer is x = 16/81. How do I get this answer?
    $\displaystyle 8x^\frac{-3}{4}=27$
    $\displaystyle x^\frac{-3}{4}=\frac{27}{8}$
    $\displaystyle -0.75logx=log\frac{27}{8}$
    $\displaystyle logx=(log\frac{27}{8})/-0.75=D$ D is just for simplicity in the last line.
    $\displaystyle 10^D=\frac{16}{81}$
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  3. #3
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    logs???

    Quote Originally Posted by JeWiSh View Post
    $\displaystyle 8x^\frac{-3}{4}=27$
    $\displaystyle x^\frac{-3}{4}=\frac{27}{8}$
    $\displaystyle -0.75logx=log\frac{27}{8}$
    $\displaystyle logx=(log\frac{27}{8})/-0.75=D$ D is just for simplicity in the last line.
    $\displaystyle 10^D=\frac{16}{81}$
    I know about applying logs but this question is located in the radical equations chapter. How do you find x using radical equations?
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  4. #4
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    Quote Originally Posted by magentarita View Post
    I found the following question in my Math B book.
    It is a radical equation problem. I played with this question for 20 minutes and got nowhere.

    Here it is:

    8x^(-3/4) = 27

    Solve for x.

    The answer is x = 16/81. How do I get this answer?

    $\displaystyle 8x^{-\frac{3}{4}}=27$

    $\displaystyle x^{-\frac{3}{4}}=\frac{27}{8}$

    $\displaystyle
    x=(\frac{27}{8})^{-\frac{4}{3}}
    $
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  5. #5
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    Just to elaborate, we're making use of the fact that:

    $\displaystyle \left(\displaystyle x^{ \displaystyle \frac{a}{b}}\right)^{ \displaystyle \frac{b}{a}} = \displaystyle x$

    So for your question, mathaddict raised both sides to the power of $\displaystyle -\tfrac{4}{3}$ .
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