Answer:
[tex]log_{9}6+3log_{9}x+5log_{9}y+2log_{9}z[/tex]
[tex]7lnx-\frac{1}{2}ln(y-1)-\frac{3}{2}lnz[/tex]
[tex]\frac{1}{3}lna+\frac{2}{3}lnb-\frac{1}{2}lny-\frac{5}{2}lnz[/tex]
Step-by-step explanation:
[tex]log_{9}(6x^{3}y^{5}z^{2})=[/tex]
[tex]log_{9}6+log_9}x^{3}+log_{9}y^{5}+log_{9}z^{2}=[/tex]
[tex]log_{9}6+3log_{9}x+5log_{9}y+2log_{9}z[/tex]
[tex]ln\frac{x^{7}}{\sqrt{(y-1)z^{3}}}=lnx^{7}-ln[(y-1)z^{3}]^{\frac{1}{2}} =[/tex]
[tex]7lnx-ln(y-1)^{\frac{1}{2}}(z^{3})^{\frac{1}{2}}}[/tex]=
[tex]7lnx-ln(y-1)^{\frac{1}{2}}-lnz^{\frac{3}{2}}=[/tex]
[tex]7lnx-\frac{1}{2}ln(y-1)-\frac{3}{2}lnz[/tex]
[tex]ln\frac{\sqrt[3]{ab^{2}}}{\sqrt{yz^{5}}}=[/tex]
[tex]ln(ab^{2})^{\frac{1}{3}}-ln(yz^{5})^{\frac{1}{2}}=[/tex]
[tex]ln(a)^{\frac{1}{3}}(b)^{\frac{2}{3}}-ln(y)^{\frac{1}{2}}(z)^{\frac{5}{2}}=[/tex]
[tex]\frac{1}{3}lna+\frac{2}{3}lnb-\frac{1}{2}lny-\frac{5}{2}lnz[/tex]
