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Math Help - WOW. This is a tough extra credit logarithem!

  1. #1
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    Cool WOW. This is a tough extra credit logarithem!

    Find the value of this is the task:

    [log base 2 (sin(11pi/6))^2]^3 + [log base 3 (tan(11pi/6))^2]^3


    All I'm going to say is that this is seems very hard.

    Forgive me if I am mistaken.

    THANKS!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Mr_Green View Post
    Find the value of this is the task:

    [log base 2 (sin(11pi/6))^2]^3 + [log base 3 (tan(11pi/6))^2]^3


    All I'm going to say is that this is seems very hard.

    Forgive me if I am mistaken.

    THANKS!
    The first think you need to know is that 11 \pi /6 is a special angle, and that:

    <br />
\sin(11 \pi /6)=-1/2<br />
and <br />
\ \ \ \tan(11 \pi /6)=-1/\sqrt{3}<br />

    so:

    <br />
[\log_2 ((\sin(11\pi /6))^2)]^3 + [\log_3(\tan(11\pi /6))^2)]^3= <br />
[\log_2 (1/2^2)]^3 + [\log_3 (1/3)]^3<br />

    ......= =[-2]^3 + [-1]^3=-9

    RonL
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