write ln[(x-4)2/(x2-1)]2/3 as a sum/difference of logs

[Red]

For x > 4, write the expression ln[(x-4)2/(x2-1)]2/3 as a sum/difference of logs. Express powers as factors.

 

[pka]

Your question is very hard to read.

Is it \(\displaystyle \
\ln \left[ {\left( {\frac{{(x - 4)^2 }}{{x^2 - 1}}} \right)^{\frac{2}{3}} } \right]?\)

 

[Red]

yes, that is how the equation is written. If you'll excuse me, I am a little new at using this web site and I'm not quite sure how to subscript, superscript,...etc.

 

[pka]

Go to the top of this page. Pull down 'Forum Help' read Karl's notes.

\(\displaystyle \L\begin{array}{rcl}
\ln \left[ {\left( {\frac{{(x - 4)^2 }}{{x^2 - 1}}} \right)^{\frac{2}{3}} } \right] & = & \frac{2}{3}\ln \left[ {\frac{{(x - 4)^2 }}{{\left( {x - 1} \right)\left( {x + 1} \right)}}} \right] \\
& = & \frac{2}{3}\left[ {2\ln (x - 4) - \ln (x - 1) - \ln (x + 1)} \right] \\
\end{array}\)