Question

Find x so that `(2/9)^3 xx (2/9)^-6 = (2/9)^(2x - 1)`

Answer 1

Given, `(2/9)^3 xx (2/9)^-6 = (2/9)^(2x - 1)`

Using law of exponents,

a^m × aⁿ = (a)^{m + n}  ...[∵ a is non-zero integer]

Then, `(2/9)^(3 - 6) = (2/9)^(2x - 1)`

⇒ `(2/9)^-3 = (2/9)^(2x - 1)`

On comparing, we get

–3 = 2x – 1

⇒ –2 = 2x

⇒ x = –1