document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204792>Question 1204792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the value of a if 7^a -7^a-5 = 117642√7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841281 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841281\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll assume the equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5Ea+-+7%5E%28a-5%29+=+117642%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"7%5Ea+-+7%5E%28a-5%29+=+117642%2Asqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It can be rewritten to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5Ea+-+7%5E%28-5%29%2A7%5Ea+=+117642%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"7%5Ea+-+7%5E%28-5%29%2A7%5Ea+=+117642%2Asqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+7%5E%28-5%29%2Ax+=++117642%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"x+-+7%5E%28-5%29%2Ax+=++117642%2Asqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+7%5Ea ALIGN=MIDDLE  ALT=\"x+=+7%5Ea\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+7%5E%28-5%29%2Ax+=++117642%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"x+-+7%5E%28-5%29%2Ax+=++117642%2Asqrt%287%29\"   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%281+-+7%5E%28-5%29%29+=++117642%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"x%281+-+7%5E%28-5%29%29+=++117642%2Asqrt%287%29\"   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%281+-+1%2F%287%5E5%29%29+=++117642%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"x%281+-+1%2F%287%5E5%29%29+=++117642%2Asqrt%287%29\"   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%281+-+1%2F16807%29+=++117642%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"x%281+-+1%2F16807%29+=++117642%2Asqrt%287%29\"   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%2816807%2F16807+-+1%2F16807%29+=++117642%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"x%2816807%2F16807+-+1%2F16807%29+=++117642%2Asqrt%287%29\"   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%28%2816807-1%29%2F16807%29+=++117642%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"x%28%2816807-1%29%2F16807%29+=++117642%2Asqrt%287%29\"   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%2816806%2F16807%29+=++117642%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"x%2816806%2F16807%29+=++117642%2Asqrt%287%29\"   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+=++%2816807%2F16806%29%2A117642%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"x+=++%2816807%2F16806%29%2A117642%2Asqrt%287%29\"   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+=++117649%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"x+=++117649%2Asqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice how 7^6 = 117649<BR>\n" );
document.write( "We can rewrite the right hand side as a power of 7.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+117649%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"x+=+117649%2Asqrt%287%29\"   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+=+7%5E6%2A7%5E%281%2F2%29%5E%22%22 ALIGN=MIDDLE  ALT=\"x+=+7%5E6%2A7%5E%281%2F2%29%5E%22%22\"   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+=+7%5E%286%2B1%2F2%29%5E%22%22 ALIGN=MIDDLE  ALT=\"x+=+7%5E%286%2B1%2F2%29%5E%22%22\"   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+=+7%5E%2813%2F2%29%5E%22%22 ALIGN=MIDDLE  ALT=\"x+=+7%5E%2813%2F2%29%5E%22%22\"   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=7%5Ea+=+7%5E%2813%2F2%29%5E%22%22 ALIGN=MIDDLE  ALT=\"7%5Ea+=+7%5E%2813%2F2%29%5E%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > plug in x = 7^a\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+13%2F2 ALIGN=MIDDLE  ALT=\"a+=+13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > The bases are both 7, so the exponents must be the same.<BR>\n" );
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