heyysn8347
heyysn8347
18-07-2019
Mathematics
contestada
Prove that log3(2) is irrational.
Respuesta :
ConcepcionPetillo
ConcepcionPetillo
25-07-2019
Step-by-step explanation:
Assume that [tex]\log _{3}2[/tex] = [tex]\frac{p}{q}[/tex] ≥ 0 then p and q are positive integers
So, it must comply with [tex]3^{p} = 2^{q}[/tex]
If p and q are positive (≥ 0), then LHS is odd and RHS is even which is a clear contradiction.
This shows that [tex]\log_{2}3[/tex] is irrational.
Hence proved
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