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Math Help - Simplifying and/or Computing problems

  1. #1
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    Simplifying and/or Computing problems

    Hi I need help simplifing these problems.

    1. 2ln sqrt(e)
    = sqrt(3)^2
    = 3

    2 ^Logx = 2^log4 x
    = 4 ^3x

    3. tan ^-1(1/ sqrt(3)
    = pi/3

    are these right?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by killasnake View Post
    1. 2ln sqrt(e)
    = sqrt(3)^2
    = 3
    Where did the 3 come from?

    2~ln(\sqrt{e}) = 2~ln \left ( e^{1/2} \right ) = 2~ \frac{1}{2} \cdot ln(e) = 1 \cdot 1 = 1

    -Dan
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by killasnake View Post
    2 ^Logx = 2^log4 x
    = 4 ^3x
    I presume "Log" is log_{10}?

    Use the change of base formula:
    log_{10}(x) = \frac{log_2(x)}{log_2(10)}

    So
    2^{log_{10}(x)} = 2^{\frac{log_2(x)}{log_2(10)}}

    = \left ( 2^{log_2(x)} \right )^{1/<br />
log_2(10)}

    = x^{1/log_2(10)} \approx x^{0.30103}

    -Dan
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by killasnake View Post
    3. tan ^-1(1/ sqrt(3)
    = pi/3
    Close.
    tan^{-1} \left ( \frac{1}{\sqrt{3}} \right ) = \frac{\pi}{6}

    -Dan
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  5. #5
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    Quote Originally Posted by topsquark View Post
    Where did the 3 come from?

    2~ln(\sqrt{e}) = 2~ln \left ( e^{1/2} \right ) = 2~ \frac{1}{2} \cdot ln(e) = 1 \cdot 1 = 1

    -Dan
    oh crap i just realised my problem... the 3 was suppose to be an e
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