Question

If 5x  - 3y = 13438 and 5x-1 + 3y+1 = 9686, then x + y equals 

Answer 1

Calculation:

5^x – 3^y = 13438      ----(i)

5^{(x – 1)} + 3^{(y + 1)} = 968

(5^x/5) + 3 × 3^y = 9686      ----(ii)

Multiplying equation 1 by 3 and adding, we get

⇒ 5^x = 15625

⇒ 5^x = 5⁶

So, x = 6

Putting x in equation 1, we get

⇒ 3^y = 2187

⇒ 3^y = 3⁷

So, y = 7

So, x + y = 7 + 6 = 13

∴ The value of x + y is 13.