document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=625447>Question 625447</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation       <BR>\n" );
document.write( "                                   16^2k= 4^k-1\r<BR>\n" );
document.write( "\n" );
document.write( "             <BR>\n" );
document.write( "and (x^1/4-6 )(x^1/2-3) = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #393581 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=393581\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I assume that you meant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5E%282k%29=+4%5E%28k-1%29 ALIGN=MIDDLE  ALT=\"16%5E%282k%29=+4%5E%28k-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16=4%5E2 ALIGN=MIDDLE  ALT=\"16=4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can write it as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%5E2%29%5E%282k%29=+4%5E%28k-1%29 ALIGN=MIDDLE  ALT=\"%284%5E2%29%5E%282k%29=+4%5E%28k-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the properties of powers, we can transform that equation into a friendlier one.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%5E2%29%5E%282k%29=+4%5E%28k-1%29 ALIGN=MIDDLE  ALT=\"%284%5E2%29%5E%282k%29=+4%5E%28k-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%282%2A2%2Ak%29=+4%5E%28k-1%29 ALIGN=MIDDLE  ALT=\"4%5E%282%2A2%2Ak%29=+4%5E%28k-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%284k%29=+4%5E%28k-1%29 ALIGN=MIDDLE  ALT=\"4%5E%284k%29=+4%5E%28k-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5Ek ALIGN=MIDDLE  ALT=\"4%5Ek\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be zero, we can divide by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5Ek ALIGN=MIDDLE  ALT=\"4%5Ek\"   DISABLED_style= \"max-width:90%; height:auto;\" > both sides of the equal sign to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%284k%29%2F4%5Ek=+4%5E%28k-1%29%2F4%5Ek ALIGN=MIDDLE  ALT=\"4%5E%284k%29%2F4%5Ek=+4%5E%28k-1%29%2F4%5Ek\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we keep using properties of powers<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%284k%29%2F4%5Ek=+4%5E%28k-1%29%2F4%5Ek ALIGN=MIDDLE  ALT=\"4%5E%284k%29%2F4%5Ek=+4%5E%28k-1%29%2F4%5Ek\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%284k-k%29=4%5E%28k-1-k%29 ALIGN=MIDDLE  ALT=\"4%5E%284k-k%29=4%5E%28k-1-k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%283k%29=4%5E%28-1%29 ALIGN=MIDDLE  ALT=\"4%5E%283k%29=4%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3k=-1 ALIGN=MIDDLE  ALT=\"3k=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=-1%2F3%29 ALIGN=MIDDLE  ALT=\"highlight%28k=-1%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "I understand that your other equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E%281%2F4%29-6+%29%28x%5E%281%2F2%29-3%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%5E%281%2F4%29-6+%29%28x%5E%281%2F2%29-3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E0.25-6+%29%28x%5E0.5-3%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%5E0.25-6+%29%28x%5E0.5-3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "(I cannot get those nasty fractional exponents to show themselves nicely).<BR>\n" );
document.write( "For that equation , I would just start by doing a change of variable, to get rid of those nasty fractional exponents.<BR>\n" );
document.write( "I can define <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E%281%2F4%29=x%5E0.25 ALIGN=MIDDLE  ALT=\"y=x%5E%281%2F4%29=x%5E0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%5E4 ALIGN=MIDDLE  ALT=\"x=y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=x%5E%281%2F2%29=x%5E0.5 ALIGN=MIDDLE  ALT=\"y%5E2=x%5E%281%2F2%29=x%5E0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I re-write the equation as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-6%29%28y%5E2-3%29=0 ALIGN=MIDDLE  ALT=\"%28y-6%29%28y%5E2-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I cannot use the solution <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-sqrt%283%29 ALIGN=MIDDLE  ALT=\"y=-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E%281%2F4%29=x%5E0.25%3E=0 ALIGN=MIDDLE  ALT=\"y=x%5E%281%2F4%29=x%5E0.25%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "The other two y solutions give me good x solutions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6 ALIGN=MIDDLE  ALT=\"y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6%5E4 ALIGN=MIDDLE  ALT=\"x=6%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1296 ALIGN=MIDDLE  ALT=\"x=1296\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%283%29 ALIGN=MIDDLE  ALT=\"y=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28sqrt%283%29%29%5E4 ALIGN=MIDDLE  ALT=\"x=%28sqrt%283%29%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9 ALIGN=MIDDLE  ALT=\"x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );