## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\displaystyle \log x-\frac{1}{2}\log y-\frac{3}{2}\log z$
.... first, write the square root as a power with exponent 1/2 $...=\displaystyle \log(\frac{x^{2}}{yz^{3}})^{1/2}\quad$... Apply the property $\log_{a}M^{p}=p\cdot\log_{a}M$ $=\displaystyle \frac{1}{2}\log\frac{x^{2}}{yz^{3}}\quad$... Apply the property $\displaystyle \log_{a}\frac{M}{N}=\log_{a}M-\log_{a}N$ $=\displaystyle \frac{1}{2}[\log x^{2}-\log(yz^{3})]\quad$... Apply the property $\log_{a}(MN)=\log_{a}M+\log_{a}N$ $=\displaystyle \frac{1}{2}[\log x^{2}-(\log y+\log z^{3})]$ $=\displaystyle \frac{1}{2}[\log x^{2}-\log y-\log z^{3}]\quad$... Apply the property $\log_{a}M^{p}=p\cdot\log_{a}M$ $=\displaystyle \frac{1}{2}[2\log x-\log y-3\log z]$ $=\displaystyle \log x-\frac{1}{2}\log y-\frac{3}{2}\log z$