document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=228323>Question 228323</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help!\r<BR>\n" );
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document.write( "If log b < 0, what can you say about b?\r<BR>\n" );
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document.write( "Thanks so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #169554 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=169554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = a positive number.\r<BR>\n" );
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document.write( "Then -x = a negative number.\r<BR>\n" );
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document.write( "log(b) < 0 implies that log(b) = -x because -x < 0.\r<BR>\n" );
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document.write( "Now log(b) = -x if and only if 10^(-x) = b.\r<BR>\n" );
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document.write( "This is by basic definition of logarithms.\r<BR>\n" );
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document.write( "10^-x is the same as 1/10^x by definition.\r<BR>\n" );
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document.write( "Since x >= 0 by definition, then the smallest 10^x could be would be 1 because 10^0 = 1. \r<BR>\n" );
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document.write( "Any other value of x > 0 would result in 10^x being greater than 1.\r<BR>\n" );
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document.write( "Example:\r<BR>\n" );
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document.write( "10^0.1 = 1.2589.....\r<BR>\n" );
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document.write( "10^0.00001 = 1.0000023026\r<BR>\n" );
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document.write( "Bottom Line is the smallest 10^x can be is 1.\r<BR>\n" );
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document.write( "Now, if 1/10^x = b, this means that the largest b can be is 1 because 1/1 = 1.\r<BR>\n" );
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document.write( "so, to answer your question:\r<BR>\n" );
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document.write( "If log(b) < 0, this means that 0 < b < 1\r<BR>\n" );
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document.write( "Some examples:\r<BR>\n" );
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document.write( "log(2) = .3...<BR>\n" );
document.write( "log(1) = 0<BR>\n" );
document.write( "log(.9) = -.04...<BR>\n" );
document.write( "log(.5) = -.301...<BR>\n" );
document.write( "log(.1) = -1<BR>\n" );
document.write( "log(0) = Error - can only take log of a number > 0\r<BR>\n" );
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document.write( "So that's the answer to your question.\r<BR>\n" );
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document.write( "log(b) < 0 if and only if b is greater than 0 and b is smaller than 1. </SPAN>\n" );
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