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Math Help - Find the equation of the inverse function..Logarithm.

  1. #1
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    Find the equation of the inverse function..Logarithm.

    1a)
    y=log_5 x
    x=log_5 y
    5^x=y
    y=5^x
    f^{-1} (x)=5^x


    b)
    y=-log_5 (-x)
    x=-log_5 (-y)
    -5^x=-y
    -y=-5^x
    f^{-1} (-x)=-5^x

    Do those seem correct?
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  2. #2
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    Quote Originally Posted by NotSoBasic View Post
    1a)
    y=log_5 x
    x=log_5 y
    5^x=y
    y=5^x
    f^{-1} (x)=5^x


    b)
    y=-log_5 (-x)
    x=-log_5 (-y)
    -5^x=-y
    -y=-5^x
    f^{-1} (-x)=-5^x

    Do those seem correct?

    I agree with the first question.

    I think the 2nd question should be
    y=-log_5 (-x)
    x=-log_5 (-y)
    -x=log_5 (-y)
    5^{-x}=-y
    -y=5^{-x}
    y=-5^{-x}
    f^{-1}=-5^{-x}
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  3. #3
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    Hello, NotSoBasic!

    The first one is correct . . .



    b) \;\;y \:=\:-\log_5 (-x)

    We have: . x \:=\:-\log_5(-y)

    Switch sides: . -\log_5(-y) \:=\:x

    Multiply by -1: . \log_5(-y) \:=\:-x

    Exponentiate: . -y \:=\:5^{-x}

    Multiply by -1: . y \:=\:-5^{-x}


    Therefore: . f^{-1}(x) \:=\:-5^{-x}



    Edit: too slow again . . .
    .
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  4. #4
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    Those make more sense, thanks guys!
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  5. #5
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    Quote Originally Posted by Soroban View Post


    Edit: too slow again . . .

    happens often to me as well.
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