document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=953289>Question 953289</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to simplify (2log2x)/2 where log2 is log base 2.  An answer sheet from my teacher shows this simplifying to log2x^2 but I think this (specifically the \"squared\" part) is wrong.  Is the teacher wrong or am I missing something here?  Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #582147 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=582147\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "    Log Rules:\r<BR>\n" );
document.write( "\n" );
document.write( "    1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28mn%29%29+=+log%28b%2C%28m%29%29+%2B+log%28b%2C%28n%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28mn%29%29+=+log%28b%2C%28m%29%29+%2B+log%28b%2C%28n%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "    2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28m%2Fn%29%29+=+log%28b%2C%28m%29%29+%96+log%28b%2C%28n%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28m%2Fn%29%29+=+log%28b%2C%28m%29%29+%96+log%28b%2C%28n%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "    3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28m%5En%29%29+=+highlight%28n+%2Alog%28b%2C%28m%29%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28m%5En%29%29+=+highlight%28n+%2Alog%28b%2C%28m%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...you need to apply this rule\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282log%282%2Cx%29%29%2F2 ALIGN=MIDDLE  ALT=\"%282log%282%2Cx%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%282%29log%282%2Cx%29%29%2Fcross%282%29 ALIGN=MIDDLE  ALT=\"%28cross%282%29log%282%2Cx%29%29%2Fcross%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28log%282%2Cx%29%29 ALIGN=MIDDLE  ALT=\"highlight%28log%282%2Cx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >..simplified using base <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "now you can change the base if you will:\r<BR>\n" );
document.write( "\n" );
document.write( "In order to evaluate a non-standard-base log, you have to use the Change-of-Base formula:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%29%29=log%28d%2C%28x%29%29%2Flog%28d%2C%28b%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%29%29=log%28d%2C%28x%29%29%2Flog%28d%2C%28b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "usually we use base <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=10 ALIGN=MIDDLE  ALT=\"d=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "so, you will have\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%29%2Flog%282%29 ALIGN=MIDDLE  ALT=\"log%28x%29%2Flog%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your teacher shows this simplifying to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%5E2%29 ALIGN=MIDDLE  ALT=\"log%282%2Cx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is wrong \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2log%282%2Cx%29 ALIGN=MIDDLE  ALT=\"2log%282%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%5E2%29 ALIGN=MIDDLE  ALT=\"log%282%2Cx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (using the rule from above, but given<BR>\n" );
document.write( " is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2log%282%2Cx%29%2F2 ALIGN=MIDDLE  ALT=\"2log%282%2Cx%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%5E2%29%2F2 ALIGN=MIDDLE  ALT=\"log%282%2Cx%5E2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > not only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%5E2%29 ALIGN=MIDDLE  ALT=\"log%282%2Cx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );