# Thread: Log and rearranging question

1. ## 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

2. Originally Posted by Paymemoney
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

3. 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 $\displaystyle (4x)^3$.

4. Originally Posted by Paymemoney
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.

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

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

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

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

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

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