Given: 2^x + 3^y = 17 and

2^x+2 – 3^y+1 = 5

Take 2^x = a and 3^y = b then the given equations reduce to

2^x + 3^y = 17 ⇒ + = 17 …… (1)

2^x . ² – 3^y . = 5 ⇒ a – b = 5 …… (2)

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Substituting b = in equation (1) we get

a + = 17 ⇒ a = 17 – =

But a = ^x - and b = ^y =

⇒ 2^x = ³ and 3^y = ²

⇒ x = and y =

∴ The solution (x, y) is (, )