Question 1

Condense each expression. 100 POINTS. Five problems.

#15
#17
#19
#21
#23

Question 2

Answer:

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

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

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

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

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

Explanation:

15)
3log_(5)x-(1)/(2)log_(5)(6-x)-4log_(5)y

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

log_(5)(x^(3))/(√((6-x))(y^(4)))

17)
2log_(5)x-(1)/(3)log_(5)z+3log_(5)y

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

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

19)
2ln(x+3)-(1)/(5)ln(2x+4)-(1)/(2)ln(x+1)

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

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

21)
2log_(5)(3x)-(1)/(4)log_(5)(z-1)+3log_(5)(5y)

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

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

23)
2-(1)/(2)log_(5)(y)-5log_(5)(z)

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

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

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