document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72883>Question 72883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use log5(2)~.4307 and log5(3)~.6826 to approximate the expression without a calculator:<BR>\n" );
document.write( "log5(18)\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52114 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=52114\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use these identities to solve\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ylog%28x%29=log%28x%29%5Ey ALIGN=MIDDLE  ALT=\"ylog%28x%29=log%28x%29%5Ey\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%29%2Blog%28y%29=log%28x%2Ay%29 ALIGN=MIDDLE  ALT=\"log%28x%29%2Blog%28y%29=log%28x%2Ay%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "If we let x=2 and y=3 for the 1st identity we get\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Alog_%5B5%5D%283%29=log_%5B5%5D%283%5E2%29=log_%5B5%5D%289%29 ALIGN=MIDDLE  ALT=\"2%2Alog_%5B5%5D%283%29=log_%5B5%5D%283%5E2%29=log_%5B5%5D%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >This gets us halfway to 18.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Alog_%5B5%5D%283%29=2%2A%280.6826%29=1.3652 ALIGN=MIDDLE  ALT=\"2%2Alog_%5B5%5D%283%29=2%2A%280.6826%29=1.3652\"   DISABLED_style= \"max-width:90%; height:auto;\" >Now plug in the approximate values<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log_%5B5%5D%282%29%2Blog_%5B5%5D%289%29=log_%5B5%5D%282%2A9%29=log_%5B5%5D%2818%29 ALIGN=MIDDLE  ALT=\"log_%5B5%5D%282%29%2Blog_%5B5%5D%289%29=log_%5B5%5D%282%2A9%29=log_%5B5%5D%2818%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Notice how this turns into log(18) using the identities.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.4307%2B1.3652=1.7959 ALIGN=MIDDLE  ALT=\"0.4307%2B1.3652=1.7959\"   DISABLED_style= \"max-width:90%; height:auto;\" >Plug in remaining values.<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E1.7959=18.00032 ALIGN=MIDDLE  ALT=\"5%5E1.7959=18.00032\"   DISABLED_style= \"max-width:90%; height:auto;\" >It's close enough to work<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log_%5B5%5D%2818%29=1.7959 ALIGN=MIDDLE  ALT=\"log_%5B5%5D%2818%29=1.7959\"   DISABLED_style= \"max-width:90%; height:auto;\" >Approximately of course </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );