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If n is a natural number such that n=P1...

If n is a natural number such that `n=P_1^(a_1)P_2^(a_2)P_3^(a_3)...P_k^(a_k)` where `p_1,p_2,...p_k` are distinct primes then minimum value of `lnn` is:

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Here, `n = P_1^ (a_1)P_2^(a_2)...P_k^(a_k)`
Here, `P_1,P_2,P_3...P_k` are all prime numbers.
We know, minimum prime number is `2`.
So, minimum value of `n` will be,
`n = 2*2*2...2to k` terms
`=> n = 2^k`
Taking logs both sides,
`=>ln n = k ln2`
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