For any natural number n, we can prove that (n power of 3, n power of 4) = (3,4). The proof is as follows: let (n power of 3, n power of 4) = x, then NX power of 3 = n power of 4, i.e. (n power of X power of 3), so x power of 3 = 4, i.e. (3,4) = X, Thus (n-th power of 3, n-th power of 4) = (3,4). (1) according to the above provisions, (3,27) = (5,1) = (2) explain the reason why equation (3,4) + (3,5) = (3,20) holds
prove:
Let (3,4) = x, (3,5) = y, (3,20) = Z, then
3^x=4,3^y=5,3^z=20
∵ 3^(x+y) = 3^x×3^y =4×5=20
That is, (3,4) + (3,5) = (3,20)
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