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Math Help - algebra 3-4 only 3 questions..

  1. #1
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    algebra 3-4 only 3 questions..

    Solve if log 4 x = -2 find X as a fraction

    Solve for x 3^2x-1 = 81^x

    find exact values Sin ( 2pi/3) Cos(3pi/4) Tan( 11pi/6)


    Please help me!
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  2. #2
    MHF Contributor alexmahone's Avatar
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    log 4 x = -2
    4x=10^{-2}
    4x=\frac{1}{100}
    x=\frac{1}{400}
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  3. #3
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    Quote Originally Posted by castanum View Post
    Solve if log 4 x = -2 find X as a fraction

    Solve for x 3^2x-1 = 81^x

    find exact values Sin ( 2pi/3) Cos(3pi/4) Tan( 11pi/6)


    Please help me!
    1. I assume that you mean

    \log_4(x)=-2 If so: Use the sides of the equation as exponents to the base 4:

    4^{\log_4(x)}=4^{-2}~\implies~x=4^{-2}~\implies~\boxed{x=\dfrac1{16}}

    2. 3^{2x-1} = 81^x

    3^{2x-1} = (3^4)^x ~\implies~ 3^{2x-1} = 3^{4x}

    Two powers with the same base are equal if the exponents are equal too:

    2x-1=4x~\implies~x=-\dfrac12

    3. Use a unit-circle to determine the values of the given terms:
    <br />
\begin{aligned} s&=\sin\left(\dfrac23 \pi\right) \cdot \cos\left(\dfrac34 \pi\right) \cdot \tan\left(\dfrac{11}6 \pi\right) \\<br />
&=\dfrac12 \sqrt{3} \cdot \left(-\dfrac12 \sqrt{2}\right) \cdot \left(-\dfrac13 \sqrt{3}\right) \\&= \dfrac14 \sqrt{2}\end{aligned}
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  4. #4
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    Thanks for your help, I think I didnt make the last question clear

    the question is:

    Find the exact value of

    a) sin(2pi/3) =

    b) Cos(3pi/4)=

    c) Tan(11pi/6) =

    Do you think you could help me this?
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  5. #5
    Super Member Gamma's Avatar
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    look carefully

    Quote Originally Posted by earboth View Post
    3. Use a unit-circle to determine the values of the given terms:
    <br />
\begin{aligned} s&=\sin\left(\dfrac23 \pi\right) \cdot \cos\left(\dfrac34 \pi\right) \cdot \tan\left(\dfrac{11}6 \pi\right) \\<br />
&=\dfrac12 \sqrt{3} \cdot \left(-\dfrac12 \sqrt{2}\right) \cdot \left(-\dfrac13 \sqrt{3}\right) \\&= \dfrac14 \sqrt{2}\end{aligned}
    While he may have misinterpreted your question, the answer is still right there. He gave you the exact values of each one right before he multiplied them out, they are even in order for you.
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  6. #6
    MHF Contributor Amer's Avatar
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    a) sin(2pi/3) = = sin\frac{\pi}{3}=\frac{\sqrt{3}}{2}

    b) Cos(3pi/4)= -\frac{1}{\sqrt{2}}

    c) Tan(11pi/6) = tan(2\pi-\frac{\pi}{6})=tan(-\frac{\pi}{6})

    since tan(2 pi + x) = tan(x)
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