Discussion

Explanation:

It is given that 5^x - 3^y = 13438 and 5^x-1 + 3^y+1 = 9686

Let 5^x-1 = k and 3^y = m

So, 5k - m = 13538        …(1)

k + 3m = 9686        …(2)

Multiply (1) with 3,

15k - 3m = 40314 ----(3)

Adding (2) and (3) we get,

16k = 50000

k = 625 × 5

k = 5⁵

We know, 5^x-1 = k

So, x - 1 = 5

x = 6

We know, k + 3m = 9686

3125 + 3m = 9686

3m = 6561

m = 2187

m = 3⁷ = 3^y

y = 7

x + y = 6 + 7 = 13

Hence, 13.

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