document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=560460>Question 560460</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve for x:\r<BR>\n" );
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document.write( "log base 3 (7x+4)-log base 3 of 2 = 2logbase3 of X </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #363886 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=363886\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%283%2C+%287x+%2B+4%29%29+-+log%283%2C2%29+=+2%2Alog%283%2Cx%29+ ALIGN=MIDDLE  ALT=\"+log%283%2C+%287x+%2B+4%29%29+-+log%283%2C2%29+=+2%2Alog%283%2Cx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the rule<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28a%29+-+log%28b%29+=+log%28a%2Fb%29+ ALIGN=MIDDLE  ALT=\"+log%28a%29+-+log%28b%29+=+log%28a%2Fb%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%283%2C++%28%287%2F2%29%2Ax+%2B+2%29+%29+=+2%2Alog%283%2Cx%29+ ALIGN=MIDDLE  ALT=\"+log%283%2C++%28%287%2F2%29%2Ax+%2B+2%29+%29+=+2%2Alog%283%2Cx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the rule<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%2Alog%28b%29+=+log%28b%5Ea%29+ ALIGN=MIDDLE  ALT=\"+a%2Alog%28b%29+=+log%28b%5Ea%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%283%2C+%28%287%2F2%29%2Ax+%2B+2%29+%29+=+log%283%2Cx%5E2%29+ ALIGN=MIDDLE  ALT=\"+log%283%2C+%28%287%2F2%29%2Ax+%2B+2%29+%29+=+log%283%2Cx%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%287%2F2%29%2Ax+%2B+2+=+x%5E2+ ALIGN=MIDDLE  ALT=\"+%287%2F2%29%2Ax+%2B+2+=+x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+%287%2F2%29%2Ax+-+2+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+%287%2F2%29%2Ax+-+2+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x%5E2+-+7x+-+4+=+0+ ALIGN=MIDDLE  ALT=\"+2x%5E2+-+7x+-+4+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+2+ ALIGN=MIDDLE  ALT=\"+a+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-7+ ALIGN=MIDDLE  ALT=\"+b+=+-7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-4+ ALIGN=MIDDLE  ALT=\"+c+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%2A2%2A%28-4%29+%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%2A2%2A%28-4%29+%29%29%2F%282%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+7+%2B-+sqrt%28+49+%2B+32+%29%29+%2F+4+ ALIGN=MIDDLE  ALT=\"+x+=+%28+7+%2B-+sqrt%28+49+%2B+32+%29%29+%2F+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+7+%2B-+sqrt%28+81+%29%29+%2F+4+ ALIGN=MIDDLE  ALT=\"+x+=+%28+7+%2B-+sqrt%28+81+%29%29+%2F+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+7+%2B+9+%29%2F4+ ALIGN=MIDDLE  ALT=\"+x+=+%28+7+%2B+9+%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+4+ ALIGN=MIDDLE  ALT=\"+x+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, taking the (-) square root,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+7+-+9+%29+%2F+4+ ALIGN=MIDDLE  ALT=\"+x+=+%28+7+-+9+%29+%2F+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-2%2F4+ ALIGN=MIDDLE  ALT=\"+x+=+-2%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-%281%2F2%29+ ALIGN=MIDDLE  ALT=\"+x+=+-%281%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+4+ ALIGN=MIDDLE  ALT=\"+x+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%283%2C+%287x+%2B+4%29%29+-+log%283%2C2%29+=+2%2Alog%283%2Cx%29+ ALIGN=MIDDLE  ALT=\"+log%283%2C+%287x+%2B+4%29%29+-+log%283%2C2%29+=+2%2Alog%283%2Cx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%283%2C+%287%2A4+%2B+4%29%29+-+log%283%2C2%29+=+2%2Alog%283%2C4%29+ ALIGN=MIDDLE  ALT=\"+log%283%2C+%287%2A4+%2B+4%29%29+-+log%283%2C2%29+=+2%2Alog%283%2C4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%283%2C+32%29+b-+log%283%2C+2%29+=+2%2Alog%283%2C4%29+ ALIGN=MIDDLE  ALT=\"+log%283%2C+32%29+b-+log%283%2C+2%29+=+2%2Alog%283%2C4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%283%2C+%2832%2F2%29%29+=+log%283%2C4%5E2%29+ ALIGN=MIDDLE  ALT=\"+log%283%2C+%2832%2F2%29%29+=+log%283%2C4%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%283%2C16%29+=+log%283%2C16%29+ ALIGN=MIDDLE  ALT=\"+log%283%2C16%29+=+log%283%2C16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "Using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-%281%2F2%29+ ALIGN=MIDDLE  ALT=\"+x+=+-%281%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%283%2C+%287%2A%28-1%2F2%29+%2B+4%29%29+-+log%283%2C2%29+=+2%2Alog%283%2C%28-1%2F2%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I have to reject this solution 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;\" > because of the <BR>\n" );
document.write( "right side. It is impossible to raise the base <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to<BR>\n" );
document.write( "some power ( + or - ) that will result in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-%281%2F2%29+ ALIGN=MIDDLE  ALT=\"+-%281%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "or any negative number.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+4+ ALIGN=MIDDLE  ALT=\"+x+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the only solution </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );