Question

If 2x=3y + 4, what is 9^x/27
The teacher gave the answer but we have to show the work

Answer 1

81

Explanation:

Rearrange
`2x=3y+4` to make y the subject:
`y=(1)/(3) (2x-4)`

Just working with the denominator of
`(9^x)/(27^y)` to rewrite it using
`x`:

`27^y=27^{(1)/(3)(2x-4)}`

`=(27^{(1)/(3)})^((2x-4))`

`=3^((2x-4))`

`=3^(2x)` ÷
`3^4`

`=(3^2)^x` ÷ 81

`=(9^(x))/(81)`

Substitute this into
`(9^x)/(27^y)` and solve:

So
`9^x` ÷
`27^y=9^x` ÷
`(9^(x))/(81)`

`=9^x * (81)/(9^x)`

`=81`