Question

Condense each expression. 100 POINTS. Five problems. #15 #17 #19 #21 #23

Answer 1

Answer:

15) $log_{5}\frac{x^{3}}{(6-x)^{\frac{1}{2}}(y)^{4}}$

17) $log_{5}\frac{x^{2}y^{3}}{z^{\frac{1}{3}}}$

19) $ln\frac{(x+3)^{2}}{(2x+4)^{\frac{1}{5}}(x+1)^{\frac{1}{2}}}$

21) $log_{5}\frac{(3x)^{2}(5y)^{3}}{(z-1)^{\frac{1}{4}}}$

23) $2-log_{5}(y)^{\frac{1}{2}}(z)^{5}}$

Step-by-step explanation:

15) $3log_{5}x-\frac{1}{2}log_{5}(6-x)-4log_{5}y$

$log_{5}x^{3}-log_{5}(6-x)^{\frac{1}{2}}-log_{5}y^{4}$

$log_{5}\frac{x^{3}}{\sqrt{(6-x)}(y^{4})}$

17) $2log_{5}x-\frac{1}{3}log_{5}z+3log_{5}y$

$log_{5}x^{2}-log_{5}z^{\frac{1}{3}}+log_{5}y^{3}$

$log_{5}\frac{(x^{2})(y^{3})}{z^{\frac{1}{3}}}$

19) $2ln(x+3)-\frac{1}{5}ln(2x+4)-\frac{1}{2}ln(x+1)$

$ln(x+3)^{2}-ln(2x+4)^{\frac{1}{5}}-ln(x+1)^{\frac{1}{2}}$

$ln\frac{(x+3)^{2} }{(2x+4)^{\frac{1}{5}}(x+1)^{\frac{1}{2}}}$

21) $2log_{5}(3x)-\frac{1}{4}log_{5}(z-1)+3log_{5}(5y)$

$log_{5}(3x)^{2}-log_{5}(z-1)^{\frac{1}{4}}+log_{5}(5y)^{3}$

$log_{5}\frac{(3x)^{2}(5y)^{3}}{(z-1)^{\frac{1}{4}}}$

23) $2-\frac{1}{2}log_{5}(y)-5log_{5}(z)$

$2-log_{5}(y)^{\frac{1}{2}}-log_{5}(z)^{5}}$

$2-log_{5}(y)^{\frac{1}{2}}(z)^{5}}$