document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73437>Question 73437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find the log of a number to any base, we can use a conversion formula\r<BR>\n" );
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document.write( "log b^a = log a<BR>\n" );
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document.write( "          log b\r<BR>\n" );
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document.write( "Using this formaul, how do I find log 2 1000. Round to the hundredth's place. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52561 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=52561\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To evaluate a log that doesn't have a base of 10, you would use the change of base formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log_%5Bb%5D%28a%29=%28log%28a%29%29%2F%28log%28b%29%29 ALIGN=MIDDLE  ALT=\"log_%5Bb%5D%28a%29=%28log%28a%29%29%2F%28log%28b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Where the logs on the right are logs of base 10. So if I have <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log_%5B2%5D%281000%29 ALIGN=MIDDLE  ALT=\"log_%5B2%5D%281000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > It would look like this with the change of base formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log_%5B2%5D%281000%29=%28log%281000%29%29%2F%28log%282%29%29 ALIGN=MIDDLE  ALT=\"log_%5B2%5D%281000%29=%28log%281000%29%29%2F%28log%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So if we evaluate log(1000) we get 3 (10^3=1000) and if we evaluate log(2) we get 0.30103 approximately<BR>\n" );
document.write( "So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log_%5B2%5D%281000%29=%28log%281000%29%29%2F%28log%282%29%29=3%2F0.30103=9.96578 ALIGN=MIDDLE  ALT=\"log_%5B2%5D%281000%29=%28log%281000%29%29%2F%28log%282%29%29=3%2F0.30103=9.96578\"   DISABLED_style= \"max-width:90%; height:auto;\" >Approximately<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log_%5B2%5D%281000%29 ALIGN=MIDDLE  ALT=\"log_%5B2%5D%281000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (or the log base 2 of 1000) is approximately equal to 9.96578<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex=1000 ALIGN=MIDDLE  ALT=\"2%5Ex=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" >If we plug in 9.96578 for x we should get 1000<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%289.96578%29=1000 ALIGN=MIDDLE  ALT=\"2%5E%289.96578%29=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=999.99999=1000 ALIGN=MIDDLE  ALT=\"999.99999=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Which is very close to true, since we have round off errors this is good enough.<BR>\n" );
document.write( "Hope this makes sense. </SPAN>\n" );
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