document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=894861>Question 894861</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear Sir/Madam, \r<BR>\n" );
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document.write( "Please help me with this logarithm problem.\r<BR>\n" );
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document.write( "If log2a + logbb  &#8805; 6, then the least value of a + b is.\r<BR>\n" );
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document.write( "note: the bases are 2 and b\r<BR>\n" );
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document.write( "Thank you very much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #542383 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=542383\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> logbb can be shown as log(b,b)<BR>\n" );
document.write( "log2a can be shown as log(2,a)\r<BR>\n" );
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document.write( "your equation is log(2,a) + log(b,b) >= 6\r<BR>\n" );
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document.write( "since log(b,b) will always be equal to 1, then b can be any legitimate value greater than 0.\r<BR>\n" );
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document.write( "since log(b,b) will always be equal to 1, your equation becomes:\r<BR>\n" );
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document.write( "log(2,a) + 1 >= 6\r<BR>\n" );
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document.write( "subtract 1 from both sides of this equation to get log(2,a) >= 5\r<BR>\n" );
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document.write( "solve for log(2,a) = 5 to get log(2,a) = 5 if and only if 2^5 = a which occurs when a = 32.\r<BR>\n" );
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document.write( "so log(2,32) = 5\r<BR>\n" );
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document.write( "that appears to be the minimum value for a.<BR>\n" );
document.write( "if a > 32, then log(2,a) will be greater than 5<BR>\n" );
document.write( "if a < 32, then log(2,a) will be less than 5.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "log(2,64) = 6 which is greater than 5.<BR>\n" );
document.write( "log(2,16) = 4 which is less than 5.\r<BR>\n" );
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document.write( "a has to be greater than or equal to 32 and b has to be greater than or equal to 0.<BR>\n" );
document.write( "therefore, a + b has to be greater than or equal to 32.\r<BR>\n" );
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document.write( "that's your solution as far as i can tell.\r<BR>\n" );
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