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Math Help - Log and rearranging question

  1. #1
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    Log and rearranging question

    Hi
    The following questions i need help on:
    1)Given u=\frac{x^2+t}{x^2-t}, find t in terms of u and x.

    2)Simplify  log\frac{4x^3}{\sqrt2}
    Note:Log is base of 2.
    Someone tell me if this is correct:
    =3log4x-\frac{1}{2}log2

    =3log4x-\frac{1}{2}

    P.S
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  2. #2
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    Quote Originally Posted by Paymemoney View Post
    Hi
    The following questions i need help on:
    1)Given u=\frac{x^2+t}{x^2-t}, find t in terms of u and x.

    2)Simplify  log\frac{4x^3}{\sqrt2}
    Note:Log is base of 2.
    Someone tell me if this is correct:
    =3log4x-\frac{1}{2}log2

    =3log4x-\frac{1}{2}

    P.S
    u(x^2-t) = x^2+t

    ux^2 - ut = x^2+t<br />

    ux^2 - x^2 = ut + t

    x^2(u-1) = t(u+1)

    \frac{x^2(u-1)}{u+1} = t



    \log(4x^3) - \log{\sqrt{2}}

    \log{4} + 3\log{x} - \frac{1}{2}\log{2}

    finish
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  3. #3
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    For 1)

    u(x^2-t)=x^2+t

    (u)x^2-ut=x^2+t

    (u)x^2-x^2=t+ut=t(u+1)

    now we have a single t, so the rest is straightforward.

    2) error as it's not (4x)^3.
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  4. #4
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    Quote Originally Posted by Paymemoney View Post
    Hi
    The following questions i need help on:
    1)Given u=\frac{x^2+t}{x^2-t}, find t in terms of u and x.

    u=\frac{x^2+t}{x^2-t}

    u(x^2-t)=x^2+t

    ux^2-tu=x^2+t

    ux^2-x^2=t+tu

    ux^2-x^2=t(1+u)

    \frac{ux^2-x^2}{1+u}=t
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