Question

Find x, if 9 x 3^x = (27) ^2x-3.

Answer 1

9 × 3^x = (27) ^2x−3

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

⇒ `3^(x + 2) = (3)^(3(2x - 3)`

`=> 3^(x + 2) = (3)^(6x - 9)`

Since, bases are same, compare them,

x + 2 = 6x − 9

6x − x = 9 + 2

`=>` 5x = 11

`=> x = 11/5  i.e. 2 1/5`