expanding log

**burner** · October 25th 2009, 10:36 AM

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.

**skeeter** · October 25th 2009, 10:52 AM

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.

$\ln\left[\frac{(2x-1)(2x+1)}{4x^2+1}\right]^{\frac{1}{5}}$

now use these three log properties ...

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

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

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

**earboth** · October 25th 2009, 10:54 AM

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:

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

And now use logarithm:

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

EDIT Beaten again ...

**burner** · October 25th 2009, 04:34 PM

ty for ur help i get it now

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