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Math Help - Log problem

  1. #1
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    Log problem

    Find the smallest real number x, correct to the nearest hundredth, which satisfies the equation:
    (log(sub 2) x)^3 - log(sub 2)(2x^3)=(log(sub 2))^2-log(sub 2)(x^2) - log(sub 2)(2)
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  2. #2
    Super Member
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    Please write this out using LaTeX i can't really read the questions properly

    \log _{2}{x^n} around the math tags gives \log _{2}{x^n}
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  3. #3
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    (log _{2}{x})^3 - log_{2}({2x^3})=(log_{2}{x})^2 - log_{2}({x^2}) - log_{2}{2}

    Like that?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by LordHz View Post
    (log _{2}{x})^3 - log_{2}({2x^3})=(log_{2}{x})^2 - log_{2}({x^2}) - log_{2}{2}

    Like that?
    you tell us, does it look like what your text says it should look like?

    anyway, simplify the logarithms first.

    you have: (\log_2 x)^3 - \log_2 2 - 3 \log_2 x = (\log_2 x)^2 - 2 \log_2 x - 1 ............(any questions about changing the logarithms?)

    now let \log_2 x be y, so you really want to solve:

    y^3 - 1 - 3y = y^2 - 2y - 1

    can you solve that?

    when done, just replace y with \log_2 x and solve for x
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