document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=771674>Question 771674</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that [1/loga (abc)] + [1/logb (abc)] + [1/logc (abc)] = 1\r<BR>\n" );
document.write( "\n" );
document.write( "My working:<BR>\n" );
document.write( " [1/log abc/log a] + [1/log abc/log b] + [1/log abc/log c] <BR>\n" );
document.write( "=[log a/log abc] + [log b/log abc] + [log c/log abc]<BR>\n" );
document.write( "=[log (a*b*c)] / [log (abc)^3]<BR>\n" );
document.write( "=log (abc) / log (abc)^3<BR>\n" );
document.write( "=1/3<BR>\n" );
document.write( " <BR>\n" );
document.write( "My answer is is 1/3, it's wrong. I should prove that the answer is equals to 1. Please help me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #470357 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=470357\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Flog%28a%2C%28abc%29%29 ALIGN=MIDDLE  ALT=\"1%2Flog%28a%2C%28abc%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Flog%28b%2C%28abc%29%29 ALIGN=MIDDLE  ALT=\"1%2Flog%28b%2C%28abc%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Flog%28c%2C%28abc%29%29=1 ALIGN=MIDDLE  ALT=\"1%2Flog%28c%2C%28abc%29%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Your working start is good:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%28log%28abc%29%2Flog%28a%29%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28%28log%28abc%29%2Flog%28a%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%28log%28abc%29%2Flog%28b%29%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28%28log%28abc%29%2Flog%28b%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%28log%28abc%29%2Flog%28c%29%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28%28log%28abc%29%2Flog%28c%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28a%29%29%2Flog%28%28abc%29%29 ALIGN=MIDDLE  ALT=\"log%28%28a%29%29%2Flog%28%28abc%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28b%29%29%2Flog%28%28abc%29%29 ALIGN=MIDDLE  ALT=\"log%28%28b%29%29%2Flog%28%28abc%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28c%29%29%2Flog%28%28abc%29%29 ALIGN=MIDDLE  ALT=\"log%28%28c%29%29%2Flog%28%28abc%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then, you forget that you are adding fractions with a common denominator, and multiply the denominators instead of leaving the common denominator alone, and just adding the numerators,like this:<BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%28%28a%29%29%2Blog%28%28b%29%29%2Blog%28%28c%29%29%29%2Flog%28%28abc%29%29 ALIGN=MIDDLE  ALT=\"%28log%28%28a%29%29%2Blog%28%28b%29%29%2Blog%28%28c%29%29%29%2Flog%28%28abc%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28abc%29%29%2Flog%28%28abc%29%29 ALIGN=MIDDLE  ALT=\"log%28%28abc%29%29%2Flog%28%28abc%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That kind of confusion happens to most of us now and then.<BR>\n" );
document.write( "Unfortunately, once we make a mistake like that we cannot detect it by ourselves.<BR>\n" );
document.write( "We need help from a pair of fresh, unbiased eyes. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );