Answer:
15) [tex]log_{5}\frac{x^{3}}{(6-x)^{\frac{1}{2}}(y)^{4}}[/tex]
17) [tex]log_{5}\frac{x^{2}y^{3}}{z^{\frac{1}{3}}}[/tex]
19) [tex]ln\frac{(x+3)^{2}}{(2x+4)^{\frac{1}{5}}(x+1)^{\frac{1}{2}}}[/tex]
21) [tex]log_{5}\frac{(3x)^{2}(5y)^{3}}{(z-1)^{\frac{1}{4}}}[/tex]
23) [tex]2-log_{5}(y)^{\frac{1}{2}}(z)^{5}}[/tex]
Step-by-step explanation:
15) [tex]3log_{5}x-\frac{1}{2}log_{5}(6-x)-4log_{5}y[/tex]
[tex]log_{5}x^{3}-log_{5}(6-x)^{\frac{1}{2}}-log_{5}y^{4}[/tex]
[tex]log_{5}\frac{x^{3}}{\sqrt{(6-x)}(y^{4})}[/tex]
17) [tex]2log_{5}x-\frac{1}{3}log_{5}z+3log_{5}y[/tex]
[tex]log_{5}x^{2}-log_{5}z^{\frac{1}{3}}+log_{5}y^{3}[/tex]
[tex]log_{5}\frac{(x^{2})(y^{3})}{z^{\frac{1}{3}}}[/tex]
19) [tex]2ln(x+3)-\frac{1}{5}ln(2x+4)-\frac{1}{2}ln(x+1)[/tex]
[tex]ln(x+3)^{2}-ln(2x+4)^{\frac{1}{5}}-ln(x+1)^{\frac{1}{2}}[/tex]
[tex]ln\frac{(x+3)^{2} }{(2x+4)^{\frac{1}{5}}(x+1)^{\frac{1}{2}}}[/tex]
21) [tex]2log_{5}(3x)-\frac{1}{4}log_{5}(z-1)+3log_{5}(5y)[/tex]
[tex]log_{5}(3x)^{2}-log_{5}(z-1)^{\frac{1}{4}}+log_{5}(5y)^{3}[/tex]
[tex]log_{5}\frac{(3x)^{2}(5y)^{3}}{(z-1)^{\frac{1}{4}}}[/tex]
23) [tex]2-\frac{1}{2}log_{5}(y)-5log_{5}(z)[/tex]
[tex]2-log_{5}(y)^{\frac{1}{2}}-log_{5}(z)^{5}}[/tex]
[tex]2-log_{5}(y)^{\frac{1}{2}}(z)^{5}}[/tex]
