Question

If (a/b)^{x - 1} = (b/a)^{x - 3} then find the value of x.

Answer 1

We have, (a/b)^{x - 1} = (b/a)^{x - 3}

⇒ (a/b)^{x - 1} = (a/b)^{-(x - 3)}

When bases are equal, exponents must be equal.

∴  x - 1 = - (x - 3)

⇒ x - 1 = - x + 3

⇒ 2x = 4

⇒ x = 2