document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175148>Question 175148</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I solve the equation for x: 64=2^3^x? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130222 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=130222\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think you mean:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64=2%5E3%5Ex ALIGN=MIDDLE  ALT=\"64=2%5E3%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Recognize that 64 is a power of 2, namely <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64=2%5E6 ALIGN=MIDDLE  ALT=\"64=2%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Hence, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E6=2%5E3%5Ex ALIGN=MIDDLE  ALT=\"2%5E6=2%5E3%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > and therefore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5Ex=6 ALIGN=MIDDLE  ALT=\"3%5Ex=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take the log of both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%283%5Ex%29%29=log%28%286%29%29 ALIGN=MIDDLE  ALT=\"log%28%283%5Ex%29%29=log%28%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28r%5Es%29%29=s%2Alog%28%28r%29%29 ALIGN=MIDDLE  ALT=\"log%28%28r%5Es%29%29=s%2Alog%28%28r%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Alog%28%283%29%29=log%28%286%29%29 ALIGN=MIDDLE  ALT=\"x%2Alog%28%283%29%29=log%28%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and finally,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=log%28%286%29%29%2Flog%28%283%29%29 ALIGN=MIDDLE  ALT=\"x=log%28%286%29%29%2Flog%28%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is the exact answer.  Use your calculator for a numerical approximation of the appropriate precision if necessary. </SPAN>\n" );
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