document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207302>Question 1207302</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The lengths of the sides of an equilateral triangle are log4(a), log10(b), log25(a+b) where A and B are positive numbers. What is the value of a/b? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845094 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=845094\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let x be the side length of the equilateral triangle.  Then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2Ca%29=x ALIGN=MIDDLE  ALT=\"log%284%2Ca%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5Ex=a ALIGN=MIDDLE  ALT=\"4%5Ex=a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2Cb%29=x ALIGN=MIDDLE  ALT=\"log%2810%2Cb%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5Ex=b ALIGN=MIDDLE  ALT=\"10%5Ex=b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2825%2Ca%2Bb%29=x ALIGN=MIDDLE  ALT=\"log%2825%2Ca%2Bb%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%5Ex=a%2Bb ALIGN=MIDDLE  ALT=\"25%5Ex=a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now look for a relationship between the three bases 4, 10, and 25: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A25+=+10%5E2 ALIGN=MIDDLE  ALT=\"4%2A25+=+10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%5Ex%29%5E2=b%5E2 ALIGN=MIDDLE  ALT=\"%2810%5Ex%29%5E2=b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%5Ex=b%5E2 ALIGN=MIDDLE  ALT=\"100%5Ex=b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%5Ex=%28100%2F4%29%5Ex=100%5Ex%2F4%5Ex ALIGN=MIDDLE  ALT=\"25%5Ex=%28100%2F4%29%5Ex=100%5Ex%2F4%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb=b%5E2%2Fa ALIGN=MIDDLE  ALT=\"a%2Bb=b%5E2%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bab=b%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bab=b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Treat this as a quadratic equation with a as the variable and solve for a using the quadratic formula.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bab-b%5E2=0 ALIGN=MIDDLE  ALT=\"a%5E2%2Bab-b%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%28-b%2Bsqrt%28b%5E2%2B4b%5E2%29%29%2F2 ALIGN=MIDDLE  ALT=\"a=%28-b%2Bsqrt%28b%5E2%2B4b%5E2%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (ignore the other solution, since a has to be positive)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%28-b%2Bsqrt%285b%5E2%29%29%2F2 ALIGN=MIDDLE  ALT=\"a=%28-b%2Bsqrt%285b%5E2%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%28-b%2Bb%2Asqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"a=%28-b%2Bb%2Asqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=b%28-1%2Bsqrt%285%29%2F2%29 ALIGN=MIDDLE  ALT=\"a=b%28-1%2Bsqrt%285%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Divide by b to find the value of a/b.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fb=%28sqrt%285%29-1%29%2F2 ALIGN=MIDDLE  ALT=\"a%2Fb=%28sqrt%285%29-1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fb=%28sqrt%285%29-1%29%2F2 ALIGN=MIDDLE  ALT=\"a%2Fb=%28sqrt%285%29-1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "------------------------------------------------------------<br><BR>\n" );
document.write( "NOTE added after seeing the response from tutor @ikleyn...<br><BR>\n" );
document.write( "This provides a good example of how a given problem is open to solving using very different equally good paths.<br><BR>\n" );
document.write( "ALWAYS be open to the possibility of solving any given problem in different ways.  Finding a different (and sometimes better) way to do something is how human knowledge increases.<br> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );