document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=550585>Question 550585</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that, log(n) >= k.log(2) (Where n >= 2 and \"k\" denote the number of distinct prime divisors of n). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #358962 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=358962\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \log(n) \ge \log(2^k) \Rightarrow n \ge 2^k\">\r<BR>\n" );
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document.write( "This is true because if we let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE n = p_1^{a_1}p_2^{a_2}...p_k^{a_k}\">, then we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE p_1^{a_1}p_2^{a_2}...p_k^{a_k} \ge 2*2*2*...*2\">, and since each prime is greater than or equal to 2, this inequality holds. </SPAN>\n" );
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