document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=623398>Question 623398</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Part V: Logarithms\r<BR>\n" );
document.write( "\n" );
document.write( "    One important application of logarithms is found in various computer search routines. For example, a binary search algorithm on a table (or array) of data takes a maximum of log2n (“log base 2, of n”) steps to complete, where n is the number of data elements that can be searched. How many steps (at most) are needed for a search of a table with 16 elements? 512 elements? Explain.<BR>\n" );
document.write( "    The approximation of the natural logarithm of 2: ln 2 &#8776; 0.693 is commonly used by applied scientists, biologists, chemists, and computer scientists. For example, chemists use it to compute the half-life of decaying substances. Based on this approximation and the power rule for logarithmic expressions, how could you approximate ln 8, without a calculator? Explain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #392072 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=392072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Starting with:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Log%5B2%5D%28n%29 ALIGN=MIDDLE  ALT=\"Log%5B2%5D%28n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute n = 16.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Log%5B2%5D%2816%29+=+Log%5B2%5D%282%5E4%29 ALIGN=MIDDLE  ALT=\"Log%5B2%5D%2816%29+=+Log%5B2%5D%282%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the power rule for logarithms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Log%5B2%5D%282%5E4%29+=+4Log%5B2%5D%282%29 ALIGN=MIDDLE  ALT=\"Log%5B2%5D%282%5E4%29+=+4Log%5B2%5D%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Recognising that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Log%5Bb%5D%28b%29+=+1 ALIGN=MIDDLE  ALT=\"Log%5Bb%5D%28b%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Log%5B2%5D%2816%29+=+4 ALIGN=MIDDLE  ALT=\"Log%5B2%5D%2816%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Similarly for n = 512 (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=512+=+2%5E9 ALIGN=MIDDLE  ALT=\"512+=+2%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" >) so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Log%28512%29+=+Log%5B2%5D%282%5E9%29 ALIGN=MIDDLE  ALT=\"Log%28512%29+=+Log%5B2%5D%282%5E9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Log%5B2%5D%282%5E9%29+=+9Log%5B2%5D%282%29 ALIGN=MIDDLE  ALT=\"Log%5B2%5D%282%5E9%29+=+9Log%5B2%5D%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ln%288%29+=+Ln%282%5E3%29 ALIGN=MIDDLE  ALT=\"Ln%288%29+=+Ln%282%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3Ln%282%29+=+3%280.693%29 ALIGN=MIDDLE  ALT=\"3Ln%282%29+=+3%280.693%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.079 ALIGN=MIDDLE  ALT=\"2.079\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );