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.
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 ...