If $5^x – 3^y = 13438$ and $5^{x-1} + 3^{y+1} = 9686$ , then what is the value of $x+y$ ?

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Official Explanation

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The first expression given to us is:

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5^x – 3^y = 13438 ……(i)

The second expression given to us is:

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5^{x-1} + 3^{y+1} = 9686

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5^x + 15* 3^y = 9686*5

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5^x + 15 * 3^y= 48430…(ii)

Subtracting expression (i) from equation (ii):

5^x + 15 * 3^y= 48430…(ii)

5^x – 3^y = 13438 ……(i)

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What this question tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Forgetting that 1 is not prime and that every integer divides 0.