I had a problem similar to this one.

Write expression as a logarithm of a single quantity and then simplify if possible.

(1/4)[log (x²-1)-log (x+1)]+3log x

Please show the steps.

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- Oct 25th 2008, 09:47 AMdc52789Just want to make sure about this logarithm problem
I had a problem similar to this one.

Write expression as a logarithm of a single quantity and then simplify if possible.

(1/4)[log (x²-1)-log (x+1)]+3log x

Please show the steps. - Oct 25th 2008, 10:20 AM11rdc11
- Oct 25th 2008, 10:24 AMdc52789
- Oct 25th 2008, 10:25 AMMoo
Hello,

Note that x>0 and |x|>1, so x>1. Otherwise it is not defined.

notice that x²-1=(x-1)(x+1)

So $\displaystyle \log(x^2-1)-\log(x+1)=\log \left(\frac{x^2-1}{x+1}\right)=\log(x-1)$

$\displaystyle \frac 14 \cdot \log(x-1)+3 \log(x)=\log \left((x-1)^{1/4}\right)+\log(x^3)$

$\displaystyle =\log \left((x-1)^{1/4} \cdot x^3\right)=\log \left((x^{13}-x^{12})^{1/4}\right)$

now it depends on how you want it to be simplified. - Oct 25th 2008, 10:37 AMdc52789
- Oct 25th 2008, 10:58 AMdc52789
- Oct 25th 2008, 11:09 AM11rdc11
- Oct 25th 2008, 11:12 AMMoo
- Oct 25th 2008, 11:18 AMdc52789