Question

Find the value of y in the equation attached to this question

Answer 1

y = 4

Explanation:

Decompose in base 3

`9^(y) =(3^(5) (3^(2))^(6) )/((3^(3))^(3) ) =(3^(5)3^(12) )/(3^(9) ) =(3^(17) )/(3^(9) ) =3^(17-9) =3^(8)`

if

`3^(8) =(3^(2) )^(4) =9^(4)`

then

`9^(y) =9^(4)`

`y=4`

Hope this helps

Answer 2

y = 4

Explanation:

1) Simplify
`3^5` to 243.

`{9}^(y)=\frac{243* {9}^(6)}{{27}^(3)}`

2) Simplify
`{9}^(6)` to 531441.

`{9}^(y)=\frac{243* 531441}{{27}^(3)}`

3) Simplify
`243* 531441` to 129140163.

`{9}^(y)=\frac{129140163}{{27}^(3)}`

4) Simplify
`{27}^(3)` to 19683.

`{9}^(y)=(129140163)/(19683)`

5) Simplify
`(129140163)/(19683)` to 6561.

`{9}^(y)=6561`

6) Convert both sides to the same base.

`9^y=9^4`

7) Cancel the base of 9 on both sides.

`y=4`

Cheers,

ROR