Question

If 3^(x-y) = 27 and 3^(x+y) = 243, find the value of x and y.

Answer 1

Given,

3^(x-y) = 27

3^(x-y) = 3³

Bases are equal hence, equate the powers (indices).

That means, x – y = 3….(i)

and

3^(x+y) = 243

3^(x+y) = 3⁵

Bases are equal hence, equate the powers (indices).

That means, x + y = 5….(ii)

Adding equations (i) and (ii), we get;

2x = 8

x = 4

Substituting x = 4 in equation (ii), we get;

4 + y = 5

y = 5 – 4 = 1

Therefore, x = 4 and y = 1.