1. ## expanding 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.

2. Originally Posted by burner
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.
$\displaystyle \ln\left[\frac{(2x-1)(2x+1)}{4x^2+1}\right]^{\frac{1}{5}}$

now use these three log properties ...

$\displaystyle \log{a^c} = c\log{a}$

$\displaystyle \log\left(\frac{a}{b}\right) = \log{a} - \log{b}$

$\displaystyle \log(ab) = \log{a} + \log{b}$

3. Originally Posted by burner
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 ...

4. ty for ur help i get it now