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Thread: Expontial functions

  1. #1
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    Expontial functions

    How does 9^x=3 nine to the x = 3

    (1/9)-x 3^2=9
    (1/3)^-2=9

    answer should be 9^(1/20
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  2. #2
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    Re: Expontial functions

    Quote Originally Posted by Melcarthus View Post
    How does 9^x=3
    answer should be 9^(1/2)


    $\displaystyle \sqrt{9}=(9)^{\tfrac{1}{2}}=3$
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  3. #3
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    Re: Expontial functions

    He4llo, Melcarthus!

    I have no idea what your steps mean.


    $\displaystyle \text{How does }\,9^x\,=\,3$
    $\displaystyle (1/9)-x \qquad\qquad 3^2\,=\,9$ . ?
    . . . . . . . . . . . . $\displaystyle \left(\tfrac{1}{3}\right)^{-2}\:=\:9$ . ?

    $\displaystyle \text{Answer should be: }\:9^{\frac{1}{2}}$ . . . . no

    We have: .$\displaystyle 9^x \;=\;3$

    . . . . . . $\displaystyle (3^2)^x \;=\;3$

    . . . . . . . $\displaystyle 3^{2x} \;=\;3^1$

    Hence: . .$\displaystyle 2x \;=\;1$

    . . . . . . . .$\displaystyle x \;=\;\tfrac{1}{2}$
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