document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=356163>Question 356163</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation 2^X=3^4-x. Write your solution exactly in terms of logarithms. Do not give a decimal approximation.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #254243 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20060)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=254243\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the equation 2^X=3^4-x. Write your solution exactly in terms of logarithms. Do not give a decimal approximation. \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex ALIGN=MIDDLE  ALT=\"2%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%22=%22%22 ALIGN=MIDDLE  ALT=\"%22%22=%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%284-x%29 ALIGN=MIDDLE  ALT=\"3%5E%284-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Take the log of both sides:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%5Ex%29 ALIGN=MIDDLE  ALT=\"log%282%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%22=%22%22 ALIGN=MIDDLE  ALT=\"%22%22=%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%5E%284-x%29%29 ALIGN=MIDDLE  ALT=\"log%283%5E%284-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Move the exponents in front of the logs:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Alog%282%29 ALIGN=MIDDLE  ALT=\"x%2Alog%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%22=%22%22 ALIGN=MIDDLE  ALT=\"%22%22=%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-x%29log%283%29 ALIGN=MIDDLE  ALT=\"%284-x%29log%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Distribute on the right\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Alog%282%29 ALIGN=MIDDLE  ALT=\"x%2Alog%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%22=%22%22 ALIGN=MIDDLE  ALT=\"%22%22=%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4log%283%29-x%2Alog%283%29 ALIGN=MIDDLE  ALT=\"4log%283%29-x%2Alog%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Get the terms that contain x on the left and other one on the right:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Alog%282%29%2Bx%2Alog%283%29 ALIGN=MIDDLE  ALT=\"x%2Alog%282%29%2Bx%2Alog%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%22=%22%22 ALIGN=MIDDLE  ALT=\"%22%22=%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4log%283%29 ALIGN=MIDDLE  ALT=\"4log%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Factor out x on the left:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28log%282%29%2Blog%283%29%29 ALIGN=MIDDLE  ALT=\"x%28log%282%29%2Blog%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%22=%22%22 ALIGN=MIDDLE  ALT=\"%22%22=%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4log%283%29 ALIGN=MIDDLE  ALT=\"4log%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%282%29%2Blog%283%29%29 ALIGN=MIDDLE  ALT=\"%28log%282%29%2Blog%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28log%282%29%2Blog%283%29%29%2F%28%28log%282%29%2Blog%283%29%29%29 ALIGN=MIDDLE  ALT=\"x%28log%282%29%2Blog%283%29%29%2F%28%28log%282%29%2Blog%283%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%22=%22%22 ALIGN=MIDDLE  ALT=\"%22%22=%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4log%283%29%2F%28%28log%282%29%2Blog%283%29%29%29 ALIGN=MIDDLE  ALT=\"4log%283%29%2F%28%28log%282%29%2Blog%283%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28cross%28log%282%29%2Blog%283%29%29%29%2F%28cross%28%28log%282%29%2Blog%283%29%29%29%29 ALIGN=MIDDLE  ALT=\"x%28cross%28log%282%29%2Blog%283%29%29%29%2F%28cross%28%28log%282%29%2Blog%283%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%22=%22%22 ALIGN=MIDDLE  ALT=\"%22%22=%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4log%283%29%2F%28log%282%29%2Blog%283%29%29 ALIGN=MIDDLE  ALT=\"4log%283%29%2F%28log%282%29%2Blog%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%22=%22%22 ALIGN=MIDDLE  ALT=\"%22%22=%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4log%283%29%2F%28log%282%29%2Blog%283%29%29 ALIGN=MIDDLE  ALT=\"4log%283%29%2F%28log%282%29%2Blog%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );