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Thread: Log and rearranging question

  1. #1
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    Log and rearranging question

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

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

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

    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 $\displaystyle u=\frac{x^2+t}{x^2-t}$, find t in terms of u and x.

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

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

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

    $\displaystyle ux^2 - ut = x^2+t
    $

    $\displaystyle ux^2 - x^2 = ut + t$

    $\displaystyle x^2(u-1) = t(u+1)$

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



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

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

    finish
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  3. #3
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    For 1)

    $\displaystyle u(x^2-t)=x^2+t$

    $\displaystyle (u)x^2-ut=x^2+t$

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

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

    2) error as it's not $\displaystyle (4x)^3$.
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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 $\displaystyle u=\frac{x^2+t}{x^2-t}$, find t in terms of u and x.

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

    $\displaystyle u(x^2-t)=x^2+t$

    $\displaystyle ux^2-tu=x^2+t$

    $\displaystyle ux^2-x^2=t+tu$

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

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