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Question 31 : If 5^{x} - 3^{y} = 13438 and 5^{x-1} + 3^{y+1} = 9686 , then x+y equals [TITA]

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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) by 3,

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

Adding (2) and (3) we get,

16k = 50000

k = 625 x 5

k = 5^{5}

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 = 3^{7 }= 3^{y}

y = 7

x + y = 6 + 7 = 13

The question is **"If 5 ^{x} - 3^{y} = 13438 and 5^{x-1} + 3^{y+1} = 9686 , then x+y equals [TITA] " **

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