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 #409257 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=409257\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I did it and also got: <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;\" >. Therefore: <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;\" > = <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;\" >\r<BR>\n" );
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document.write( "This is the correct answer and can be proven as follows:\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 ALIGN=MIDDLE  ALT=\"5%5E%283log%2825%2Ca%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------ <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;\" >\r<BR>\n" );
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document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > for a in <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;\" > results in: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28log%2825%2C25%5E3%29%29 ALIGN=MIDDLE  ALT=\"5%5E%28log%2825%2C25%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2825%2C25%5E3%29 ALIGN=MIDDLE  ALT=\"log%2825%2C25%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28log%2825%2C25%5E3%29%29 ALIGN=MIDDLE  ALT=\"5%5E%28log%2825%2C25%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E3 ALIGN=MIDDLE  ALT=\"5%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28125%29 ALIGN=MIDDLE  ALT=\"highlight%28125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > for a into the simplified version/answer of <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;\" > gives us: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%5E%283%2F2%29 ALIGN=MIDDLE  ALT=\"25%5E%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2825%29%29%5E3 ALIGN=MIDDLE  ALT=\"%28sqrt%2825%29%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E3 ALIGN=MIDDLE  ALT=\"5%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28125%29 ALIGN=MIDDLE  ALT=\"highlight%28125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "This clearly proves that your 1st answer that <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;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28a%5E%283%2F2%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28a%5E%283%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is unequivocally 100% correct. \r<BR>\n" );
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document.write( "Send comments and “thank-yous” to “D” at MathMadEzy@aol.com </SPAN>\n" );
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