proof-that-log-2-3-is-irrational-

Question Number 552 by 123456 last updated on 25/Jan/15

p r o o f t h a t \log_{2} 3 i s i r r a t i o n a l

Answered by prakash jain last updated on 25/Jan/15

Let us say \log_{2} 3 is rational, then

\log_{2} 3 = \frac{p}{q}, p, q \in N

3 = 2^{\frac{p}{q}} \Rightarrow 3^{q} = 2^{p}

which is not possible . Hencr \log_{2} 3 is irrational .