document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204250>Question 1204250</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let x be a real number such that 625^x=64 Then<BR>\n" );
document.write( "125x=a√b. What are a and b? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840380 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=840380\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+ ALIGN=MIDDLE  ALT=\"x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >be a real number such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=625%5Ex=64+ ALIGN=MIDDLE  ALT=\"625%5Ex=64+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125%5Ex=a%2Asqrt%28b%29 ALIGN=MIDDLE  ALT=\"125%5Ex=a%2Asqrt%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > What are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+ ALIGN=MIDDLE  ALT=\"a+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
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document.write( "We have the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=625%5Ex+=+64 ALIGN=MIDDLE  ALT=\"625%5Ex+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To simplify the equation, we can express both sides with the same base. We know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=625 ALIGN=MIDDLE  ALT=\"625\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be expressed as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E4 ALIGN=MIDDLE  ALT=\"5%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be expressed as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E6 ALIGN=MIDDLE  ALT=\"2%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Rewriting the equation, we have \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%5E4%29%5Ex+=+2%5E6 ALIGN=MIDDLE  ALT=\"%285%5E4%29%5Ex+=+2%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using the property of exponents, we can simplify further:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%284x%29+=+2%5E6 ALIGN=MIDDLE  ALT=\"5%5E%284x%29+=+2%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we need to equate the exponents:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+=+6 ALIGN=MIDDLE  ALT=\"4x+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, solving for<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x ALIGN=MIDDLE  ALT=\"+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6%2F4 ALIGN=MIDDLE  ALT=\"x+=+6%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, we can calculate the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125%5Ex ALIGN=MIDDLE  ALT=\"125%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+ ALIGN=MIDDLE  ALT=\"x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >we found:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125%5E%286%2F4%29=125%5E%283%2F2%29 ALIGN=MIDDLE  ALT=\"125%5E%286%2F4%29=125%5E%283%2F2%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=125=5%5E3 ALIGN=MIDDLE  ALT=\"125=5%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%5E3%29%5E%283%2F2%29=5%5E%283%283%2F2%29%29=5%5E%289%2F2%29 ALIGN=MIDDLE  ALT=\"%285%5E3%29%5E%283%2F2%29=5%5E%283%283%2F2%29%29=5%5E%289%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125%5Ex+=+sqrt%285%5E9%29 ALIGN=MIDDLE  ALT=\"125%5Ex+=+sqrt%285%5E9%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=sqrt%285%5E9%29=sqrt%28%285%5E4%29%5E2%2A5%29=5%5E4%2Asqrt%285%29=625sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%5E9%29=sqrt%28%285%5E4%29%5E2%2A5%29=5%5E4%2Asqrt%285%29=625sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125%5Ex+=+625sqrt%285%29 ALIGN=MIDDLE  ALT=\"125%5Ex+=+625sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, comparing to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125%5Ex=a%2Asqrt%28b%29 ALIGN=MIDDLE  ALT=\"125%5Ex=a%2Asqrt%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=625 ALIGN=MIDDLE  ALT=\"a=625\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5 ALIGN=MIDDLE  ALT=\"b=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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