Question

Find x.

`(2/5)^(2x + 6) xx (2/5)^3 = (2/5)^(x + 2)`

Answer 1

We have, `(2/5)^(2x + 6) xx (2/5)^3 = (2/5)^(x + 2)`

Using law of exponents,

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

Then, `(2/5)^(2x + 6 + 3) = (2/5)^(x + 2)`

On comparing powers of `(2/5)`, we get

2x + 6 + 3 = x + 2

⇒ 2x + 9 = x + 2

⇒ x = –7