x^0=1. Prove it how it is done without log process
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In short, the multiplicative identity is the number 1, because for any other number x, 1*x= x. So, the reason that any number to the zero power is one is because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1.
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x^0 = 1
x^(1-1) = 1
x^1 {x^(-1)} =1
x^1/x^1 = 1
x/x = 1
1 = 1 proved ☺
x^(1-1) = 1
x^1 {x^(-1)} =1
x^1/x^1 = 1
x/x = 1
1 = 1 proved ☺
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