# expanding log

• Oct 25th 2009, 11:36 AM
burner
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.
• Oct 25th 2009, 11:52 AM
skeeter
Quote:

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 ...

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

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

$\log(ab) = \log{a} + \log{b}$
• Oct 25th 2009, 11:54 AM
earboth
Quote:

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 ...(Crying)
• Oct 25th 2009, 05:34 PM
burner
ty for ur help i get it now