Solution
Let $$\log_{5}{2}$$ = y
Let us assume $$\log_{5}{2}$$ is a rational number.
$$\log_{5}{2}$$ = p/q, where p and q are co primes.
5^(p/q)=2 => 5^p=2^q.
5^p=5*5*5*5*5*5*5..................p times
2^p=2*2*2*2*2*2*2..................q times
No value of p and q can satisfy the equation. Hence y is an irrational number.
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