Question

Question #81caf

Answer 1

`x=1/2`

Explanation:

Note that `9^(x+2)` is the same as `9^x xx9^2`

Subtract `9^x` from both sides

`(9^x xx9^2)-9^x=240`

Factor out the `9^x`

`9^x(9^2-1)=240`

Note that `9^2=81" so "9^2-1=80`

`9^x=(24cancel(0))/(8cancel0) = 24/8=3`

Note that `sqrt(9)=9^(1/2)=3`

Thus `x=1/2`

Answer 2

x = 1/2

Explanation:

`9^(x+2) = 240 + 9^x`
`9^x * 9^2 = 240 + 9^x`
`9^x * 9^2 -9^x * 1 =240`
`9^x * (81-1) = 240`
`9^x = 240/80 = 3`
`rarr x = 1/2`