i need help expanding this expression as in rewrite it with multiple logs

ln 5√(4x²-1/4x²+1)

the 5√ is a 5th root.

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- Oct 25th 2009, 10:36 AMburnerexpanding log
i need help expanding this expression as in rewrite it with multiple logs

ln 5√(4x²-1/4x²+1)

the 5√ is a 5th root.

- Oct 25th 2009, 10:52 AMskeeter
- Oct 25th 2009, 10:54 AMearboth
1. Re-write the given term:

$\displaystyle \sqrt[5]{\dfrac{4x^2-1}{4x^2+1}} = \left((2x-1)(2x+1)(4x^2+1)^{-1} \right)^{\frac15}$

And now use logarithm:

$\displaystyle \log\left(\sqrt[5]{\dfrac{4x^2-1}{4x^2+1}} \right) = \dfrac15 \left(\log(2x-1) + \log(2x+1) - \log(4x^2+1)\right)$

EDIT Beaten again ...(Crying) - Oct 25th 2009, 04:34 PMburner
ty for ur help i get it now