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Math Help - Logarithm

  1. #1
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    Logarithm

    How would you find the values of x for these logarithms:

    a. log_x \frac {1}{5} = -\frac {1}{4}
    b. log_x 81 = \frac {3}{4}

    I put both of them in exponential form:

    a. x^\frac {-1}{4} = \frac {1}{5}
    b. x^\frac {4}{3} = 81

    Then I got stuck in trying to figure out what the value of "x" equals. I knw how to find it using a calculator but I can't find the value without using a calculator.

    And one more thing. How do you find the inverse fuction of f(x)=2log_2 x?
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  2. #2
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    Quote Originally Posted by chrozer View Post
    How would you find the values of x for these logarithms:

    a. log_x \frac {1}{5} = -\frac {1}{4}
    b. log_x 81 = \frac {3}{4}

    I put both of them in exponential form:

    a. x^\frac {-1}{4} = \frac {1}{5}
    b. x^\frac {4}{3} = 81

    Then I got stuck in trying to figure out what the value of "x" equals. I knw how to find it using a calculator but I can't find the value without using a calculator.

    And one more thing. How do you find the inverse fuction of f(x)=2log_2 x?
    for a) use exponent laws and raise each side to -4th power

    (x^\frac {-1}{4})^{-4} = (\frac {1}{5})^{-4} \iff x=5^4=625

    for b.

    x^{4/3}=81 \iff x^{4/3}=3^4 raise each side to the 3/4th power

    (x^{4/3})^{3/4}=(3^4)^{3/4} \iff x=3^3=27

    Yeah!!
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  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    forgot the last one... :(

    <br />
f(x)=2log_2 x<br />

    y=2\log_2(x) exchange x and y and solve for y

    x=2\log_2(y) \iff \frac{x}{2}=\log_2(y) \iff 2^{\frac{x}{2}}=y

    So the inverse is

    f^{-1}(x)=2^{\frac{x}{2}}
    Last edited by TheEmptySet; March 31st 2008 at 02:18 PM. Reason: LaTex typo
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  4. #4
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    Quote Originally Posted by TheEmptySet View Post
    for a) use exponent laws and raise each side to -4th power

    (x^\frac {-1}{4})^{-4} = (\frac {1}{5})^{-4} \iff x=5^4=625

    for b.

    x^{4/3}=81 \iff x^{4/3}=3^4 raise each side to the 3/4th power

    (x^{4/3})^{3/4}=(3^4)^{3/4} \iff x=3^3=27

    Yeah!!
    Thanks alot! One more thing - How do you find the inverse of f(x)=2log_2 x?

    EDIT- Ok I see now. Thnx very much!
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