Question

If `(9^(x-2) * 3^(2x-2))/(27^(x+3)) =81, x=?`

Answer 1

`x=19`

Explanation:

Given

`9^(x-2) × 3^(2x-2)/(27^(x+3))=81`

Now,we can write, `9^(x-2)=3^(2(x-2))=3^(2x-4)`

Also, `27^(x+3)=3^(3(x+3))=3^(3x+9)`

Now using the above modifications, we can write the entire equation as,

`3^(2x-4)×3^(2x-2)/3^(3x+9)=81`

Or, `3^(2x-4+2x-2-3x-9)=3^4`

Or, `3^(x-15)=3^4`

So, comparing we can write,

`x-15=4`

Or, `x=19`

Answer 2

`x=19`

Explanation:

`9^(x-2)*3^(2x-2)-:27^(x+3)=81`

`:.(3^2)^(x-2)*3^(2x-2)-:(3^3)^(x+3)=3^4`

`:.3^(2x-4)*3^(2x-2)-:3^(3(x+3))=3^4`

`:.(3^(4x-6))/(3^(3x+9))=3^4`

`:.3^(4x-6-3x-9)=3^4`

`:.3^(x-15)=3^4`

`:.x-15=4`

`:.x=15+4`

`:.x=19`