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Math Help - Textbook questions i had trouble with

  1. #1
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    Textbook questions i had trouble with

    Hey, these are questions i had trouble with

    Solve the following for x,

    b. log e (5x) - log e (3-2x) +1
    c. Log e (x) + log e (3x+1)=1
    d. (8e^-x) - e^x =2

    Simplify,
    a. 1+ log10 a - (1/3)log10 b
    b. log2 x -2log2 y + log2(xy^2)

    Evaluate,
    a. log2 square root 2 + log2 1 +2log2 2


    Thanks
    Last edited by chaneliman; April 12th 2008 at 12:16 AM.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by chaneliman View Post
    Hey, these are questions i had trouble with

    Solve the following for x,
    a. 2 log e (x+5) =6
    b. log e (5x) - log e (3-2x) +1
    c. Log e (x) + log e (3x+1)=1
    d. (8e^-x) - e^x =2

    Simplify,
    a. 1+ log10 a - (1/3)log10 b
    b. log2 x -2log2 y + log2(xy^2)

    Evaluate,
    a. log2 square root 2 + log2 1 +2log2 2
    b. 2log10 5 + 2log10 2 +1

    Thanks
    Here are a few c) from the first group
    \log_e(x)+\log_e(3x+1)=1 rewrite using prop of logs

    \log_e(x[3x+1])=1 \iff x(3x+1)=e \iff 3x^2+x-e=0

    using the quadratic formula we get

    x=\frac{-1 \pm\sqrt{1-4(4)(-e)}}{2(3)}=\frac{-1 \pm \sqrt{1+16e}}{6}

    b) from the second group

    \log_2(x)-2\log_2(y)+\log_2(xy^2) \iff \log_2(x)-\log_2(y^2)+\log(xy^2)

    \log_2(\frac{x}{y^2})+\log_2(xy^2)=\log_2(\frac{x}  {y^2}\cdot xy^2)=\log_2(x^2)
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  3. #3
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    yea i get those 2 now , but i'm still a little confused with the others
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