Problem in number theory using logarithms.

Question:-

If n is a natural number such than $n=p_1^{a_1}.p_2^{a_2}.p_3^{a_3}.......p_k^{a_k}$ and $p_1,p_2,...p_k$ are distinct primes, then show that $log(n)>=klog(2)$.

What I think is p1 is greater than or equal to 2. So is p2 and all the way to pn. So their product should be greater than and equal to $2^{k}$. Is this proof sufficient?

Source: IIT JEE 1984

• Yes, it is correct. – TBTD Apr 23 '17 at 19:04
• Yes you're right. – Iti Shree Apr 23 '17 at 19:20
• Yes.It's right... If you write p_1 then iwith dollar signs you get $p_1$ which is better than $p1$. ... Click on Help at the top bar, choose the Help Center, choose the Q "How can I format mathematics here?" – DanielWainfleet Apr 23 '17 at 23:04
• @user254665 Thank you. i did check the post, but it had very few examples. – Reeshabh Ranjan Apr 24 '17 at 3:09
• Did you go to the bottom line and click on the MathJax quick reference? – DanielWainfleet Apr 25 '17 at 2:28