document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=655680>Question 655680</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I get different answers depending on how I simplify the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%283log%2825%2Ca%29%29 ALIGN=MIDDLE  ALT=\"5%5E%283log%2825%2Ca%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This shows me that I must be awfully confused about log rules. WolframAlpha gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%283%2F2%29 ALIGN=MIDDLE  ALT=\"a%5E%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which I figured out can be done thusly:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%283log%2825%2Ca%29%29=x ALIGN=MIDDLE  ALT=\"5%5E%283log%2825%2Ca%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3log%2825%2Ca%29=log%285%2Cx%29 ALIGN=MIDDLE  ALT=\"3log%2825%2Ca%29=log%285%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3log%285%2Ca%29%2Flog%285%2C25%29=log%285%2Cx%29 ALIGN=MIDDLE  ALT=\"3log%285%2Ca%29%2Flog%285%2C25%29=log%285%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F2%29%2Alog%285%2Ca%29=log%285%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%283%2F2%29%2Alog%285%2Ca%29=log%285%2Cx%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%285%2C%28a%5E%283%2F2%29%29%29=log%285%2Cx%29 ALIGN=MIDDLE  ALT=\"log%285%2C%28a%5E%283%2F2%29%29%29=log%285%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%283%2F2%29=x ALIGN=MIDDLE  ALT=\"a%5E%283%2F2%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If I do it another way, I get my answer as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3-25 ALIGN=MIDDLE  ALT=\"a%5E3-25\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Here is how I did that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%283log%2825%2Ca%29%29=5%5Elog%2825%2C%28a%5E3%29%29=5%5E%28log%285%2C%28a%5E3%29%29%2Flog%285%2C25%29%29=5%5E%28log%285%2C%28a%5E3-25%29%29%29=a%5E3-25 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But if I do it another way, I get the answer as 5^(2/3)+a. See:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%283log%2825%2Ca%29%29=x ALIGN=MIDDLE  ALT=\"5%5E%283log%2825%2Ca%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3log%2825%2Ca%29=log%285%2Cx%29 ALIGN=MIDDLE  ALT=\"3log%2825%2Ca%29=log%285%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=log%285%2Cx%29%2Flog%2825%2Ca%29 ALIGN=MIDDLE  ALT=\"3=log%285%2Cx%29%2Flog%2825%2Ca%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=log%285%2Cx%29%2F%28log%285%2Ca%29%2Flog%285%2C25%29%29 ALIGN=MIDDLE  ALT=\"3=log%285%2Cx%29%2F%28log%285%2Ca%29%2Flog%285%2C25%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=3=log%285%2Cx%29%2Flog%285%2C%28a-25%29%29 ALIGN=MIDDLE  ALT=\"3=log%285%2Cx%29%2Flog%285%2C%28a-25%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=3=log%285%2C%28x-a%2B25%29%29 ALIGN=MIDDLE  ALT=\"3=log%285%2C%28x-a%2B25%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=5%5E3=x-a%2B25 ALIGN=MIDDLE  ALT=\"5%5E3=x-a%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E3-25%2Ba=x ALIGN=MIDDLE  ALT=\"5%5E3-25%2Ba=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2Ba=x ALIGN=MIDDLE  ALT=\"100%2Ba=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And even a third answer:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%283log%2825%2Ca%29%29=x ALIGN=MIDDLE  ALT=\"5%5E%283log%2825%2Ca%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3log%2825%2Ca%29=log%285%2Cx%29 ALIGN=MIDDLE  ALT=\"3log%2825%2Ca%29=log%285%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3log%285%2Ca%29%2Flog%285%2C25%29=log%285%2Cx%29 ALIGN=MIDDLE  ALT=\"3log%285%2Ca%29%2Flog%285%2C25%29=log%285%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F2%29%2Alog%285%2Ca%29=log%285%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%283%2F2%29%2Alog%285%2Ca%29=log%285%2Cx%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=3%2F2=log%285%2Cx%29%2Flog%285%2Ca%29 ALIGN=MIDDLE  ALT=\"3%2F2=log%285%2Cx%29%2Flog%285%2Ca%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2=log%285%2C%28x-a%29%29 ALIGN=MIDDLE  ALT=\"3%2F2=log%285%2C%28x-a%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=5%5E%283%2F2%29=x-a ALIGN=MIDDLE  ALT=\"5%5E%283%2F2%29=x-a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%283%2F2%29%2Ba=x ALIGN=MIDDLE  ALT=\"5%5E%283%2F2%29%2Ba=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #409229 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=409229\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I get different answers depending on how I simplify the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%283log%2825%2Ca%29%29 ALIGN=MIDDLE  ALT=\"5%5E%283log%2825%2Ca%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "===========================<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%283log%2825%2Ca%29%29 ALIGN=MIDDLE  ALT=\"5%5E%283log%2825%2Ca%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=5%5E%28log%2825%2Ca%5E3%29%29 ALIGN=MIDDLE  ALT=\"5%5E%28log%2825%2Ca%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since 25 = 5^2:<BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28log%285%2Ca%5E6%29%29 ALIGN=MIDDLE  ALT=\"5%5E%28log%285%2Ca%5E6%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=a%5E6 ALIGN=MIDDLE  ALT=\"a%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );