(M2)prove log5 is a irrational number?
回答 (2)
2016-03-31 9:38 am
If log5 is a rational number , let log5 = a/b , were the H.C.F. of integers 0 < a < b is 1.
10^(a/b) = 5
10ᵃ = 5ᵇ
2ᵃ = 5ᵇ⁻ᵃ
It is impossible for the H.C.F. of 2 and 5 is 1 , but a and b-a are positive integers.
So log5 is an irrational number.
10^(a/b) = 5
10ᵃ = 5ᵇ
2ᵃ = 5ᵇ⁻ᵃ
It is impossible for the H.C.F. of 2 and 5 is 1 , but a and b-a are positive integers.
So log5 is an irrational number.
2016-04-03 3:33 pm
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