document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31804>Question 31804</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the difference[s] in common logarithms.natural logarithms, and numerical logarithms </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18398 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=18398\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%5E2+=+100+ ALIGN=MIDDLE  ALT=\"+10%5E2+=+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28100%29+=+2+ ALIGN=MIDDLE  ALT=\"+log%28100%29+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%5E3+=+1000+ ALIGN=MIDDLE  ALT=\"+10%5E3+=+1000+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%281000%29+=+3+ ALIGN=MIDDLE  ALT=\"+log%281000%29+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%5E4+=+10000+ ALIGN=MIDDLE  ALT=\"+10%5E4+=+10000+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%2810000%29+=+4+ ALIGN=MIDDLE  ALT=\"+log%2810000%29+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%5E5+=+100000+ ALIGN=MIDDLE  ALT=\"+10%5E5+=+100000+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28100000%29+=+5+ ALIGN=MIDDLE  ALT=\"+log%28100000%29+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "These are logs to base 10...possibly your \"common logs\"?\r<BR>\n" );
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document.write( "We can do logs to any base. The following are logs to base2... written by me as log_2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5E2+=+4+ ALIGN=MIDDLE  ALT=\"+2%5E2+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log_2%284%29+=+2+ ALIGN=MIDDLE  ALT=\"+log_2%284%29+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5E3+=+8+ ALIGN=MIDDLE  ALT=\"+2%5E3+=+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log_2%288%29+=+3+ ALIGN=MIDDLE  ALT=\"+log_2%288%29+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5E4+=+16+ ALIGN=MIDDLE  ALT=\"+2%5E4+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log_2%2816%29+=+4+ ALIGN=MIDDLE  ALT=\"+log_2%2816%29+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5E5+=+32+ ALIGN=MIDDLE  ALT=\"+2%5E5+=+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log_2%2832%29+=+5+ ALIGN=MIDDLE  ALT=\"+log_2%2832%29+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now one particular number is 2.7182818284590.... is a number that goes on forever...has no end, so how can we write it? Well, we give it a \"name\", calling it e.\r<BR>\n" );
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document.write( "When the log base is the number e, these are called natural logs, since a lot of things in nature follow the mathematical curve of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=e%5Ex ALIGN=MIDDLE  ALT=\"y=e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Natural logs are written as ln, eg ln(10) = 2.302585...\r<BR>\n" );
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document.write( "Hope this helps.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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