document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=977126>Question 977126</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the following is the greatest?<BR>\n" );
document.write( "a. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E210 ALIGN=MIDDLE  ALT=\"3%5E210\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5E140 ALIGN=MIDDLE  ALT=\"7%5E140\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%5E105 ALIGN=MIDDLE  ALT=\"17%5E105\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=31%5E84 ALIGN=MIDDLE  ALT=\"31%5E84\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "Please give detailed solution.<BR>\n" );
document.write( "(NOTE: Don't use logarithm. It has been removed from syllabus, and I have to make my students understand without using log) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #598662 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=598662\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Which of the following is the greatest?<BR>\n" );
document.write( "a. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E210 ALIGN=MIDDLE  ALT=\"3%5E210\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5E140 ALIGN=MIDDLE  ALT=\"7%5E140\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%5E105 ALIGN=MIDDLE  ALT=\"17%5E105\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=31%5E84 ALIGN=MIDDLE  ALT=\"31%5E84\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
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document.write( "3^210 = 9^105, obviously less than 17^105, so a is eliminated.<BR>\n" );
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document.write( "Using a calculator:<BR>\n" );
document.write( "7^140 = 2.059e118<BR>\n" );
document.write( "17^105 = 1.57e129<BR>\n" );
document.write( "31^84 = 1.88e125<BR>\n" );
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document.write( "c wins again.<BR>\n" );
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document.write( "You can change them all to the same base, eg, 7, but that would require either logs or a calculator.<BR>\n" );
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document.write( "eg,<BR>\n" );
document.write( "7^140 = (2^2.8)^140 = 2^392<BR>\n" );
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document.write( "ooooooooooooooh, John's answer is cool.<BR>\n" );
document.write( "I might have figured that out eventually.<BR>\n" );
document.write( "I should have spotted that 3, 7, 17 & 31 are all 2^n plus or minus 1.<BR>\n" );
document.write( "In short, his solution is elegant.<BR>\n" );
document.write( "Probably with assistance from Satan, since we all know god is stupid. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );