expanding expression for log: ln[(radicalx)(y^2)/(z^1/2)]

[Guest]

ln[(radicalx)(y^2)/(z^1/2)]

how do you simplify a problem such as this one? i've forgotten whether or not if by radicalx, it means the same thing as x^1/2 (by radical, i mean a square root symbol )

 

[skeeter]

yes ... \(\displaystyle \L \sqrt{x} = x^{\frac{1}{2}}\)

I suspect that an expansion of the log is in order rather than a "simplification".

\(\displaystyle \L \ln{\left(\frac{\sqrt{x} y^2}{\sqrt{z}}\right)} =\)

\(\displaystyle \L \ln{\sqrt{x}} + \ln{y^2} - \ln{\sqrt{z}} =\)

\(\displaystyle \L \frac{1}{2}\ln{x} + 2\ln{y} - \frac{1}{2}\ln{z}\)