Respuesta :

Answer:

y = 4

Step-by-step explanation:

1) Simplify [tex]3^5[/tex] to 243.

[tex]{9}^{y}=\frac{243\times {9}^{6}}{{27}^{3}}[/tex]

2) Simplify [tex]{9}^{6}[/tex] to 531441.

[tex]{9}^{y}=\frac{243\times 531441}{{27}^{3}}[/tex]

3)  Simplify  [tex]243\times 531441[/tex] to  129140163.

[tex]{9}^{y}=\frac{129140163}{{27}^{3}}[/tex]

4) Simplify  [tex]{27}^{3}[/tex]  to  19683.

[tex]{9}^{y}=\frac{129140163}{19683}[/tex]

5) Simplify  [tex]\frac{129140163}{19683}[/tex] to 6561.

[tex]{9}^{y}=6561[/tex]

6) Convert both sides to the same base.

[tex]9^y=9^4[/tex]

7)  Cancel the base of 9 on both sides.

[tex]y=4[/tex]

Cheers,

ROR

profereyes12122

Answer:

y = 4

Step-by-step explanation:

Decompose  in base 3

[tex]9^{y} =\frac{3^{5} (3^{2})^{6} }{(3^{3})^{3} } =\frac{3^{5}3^{12} }{3^{9} } =\frac{3^{17} }{3^{9} } =3^{17-9} =3^{8}[/tex]

if

[tex]3^{8} =(3^{2} )^{4} =9^{4}[/tex]

then

[tex]9^{y} =9^{4}[/tex]

[tex]y=4[/tex]

Hope this helps