Working mod 3 we have (-1)^x\equiv 1 \pmod 3
So x is even say 2n
So we have ^{2n} - 3^{2n} = 16
Or (5^n+3^n)(5^n-3^n) =16
On LHS both are even and unequal and 1st term is larget and 16 need to be factored into 2 even numbers 8 * 2
So 5^n +3^n = 8
5^n - 3^n = 2
Adding we get 2* 5^n = 10 or n = 1 so x = 2
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