Question

The number of solutions of 3^{x + y} = 243 and 243^{x - y} = 3 is ______.

Options

• 0

• 1

• 2

• infinite

Answer 1

The number of solutions of 3^{x + y} = 243 and 243^{x - y} = 3 is 1.

Explanation:-

3^{x + y} = 243 = 3⁵

So x + y = 5 ....(1)

243^{x - y} = 3

(3⁵)^{x - y} = 3¹

So 5x - 5y = 1 ....(2)

Since : `a_1/a_2neb_1/b_2`, so unique solution