(M2)prove log5 is a irrational number?

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.

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