document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=743558>Question 743558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the two values of x that satisfy the equation:\r<BR>\n" );
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document.write( "2log(base4)X-log(base4)(3X-4))=1/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #452966 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=452966\">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=+2%2Alog%284%2Cx%29+-+log%284%2C+3x+-+4%29+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+2%2Alog%284%2Cx%29+-+log%284%2C+3x+-+4%29+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "The key is to make the substitution<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F2+=+log%28+4%2C2+%29+ ALIGN=MIDDLE  ALT=\"+1%2F2+=+log%28+4%2C2+%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%284%2Cx%5E2%29+-+log%284%2C+3x+-+4%29+=+log%28+4%2C2+%29+ ALIGN=MIDDLE  ALT=\"+log%284%2Cx%5E2%29+-+log%284%2C+3x+-+4%29+=+log%28+4%2C2+%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%28+4%2C+%28x%5E2+%2F+%28+3x+-+4%29%29+%29+=+log%28+4%2C2+%29+ ALIGN=MIDDLE  ALT=\"+log%28+4%2C+%28x%5E2+%2F+%28+3x+-+4%29%29+%29+=+log%28+4%2C2+%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%5E2+%2F+%28+3x-4+%29++=+2+ ALIGN=MIDDLE  ALT=\"+x%5E2+%2F+%28+3x-4+%29++=+2+\"   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+=+2%2A%28+3x-4+%29+ ALIGN=MIDDLE  ALT=\"+x%5E2+=+2%2A%28+3x-4+%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%5E2+=+6x+-+8+ ALIGN=MIDDLE  ALT=\"+x%5E2+=+6x+-+8+\"   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+-+6x+%2B+8+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+6x+%2B+8+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+x+-+4+%29%2A%28+x+-+2+%29+=+0+ ALIGN=MIDDLE  ALT=\"+%28+x+-+4+%29%2A%28+x+-+2+%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( by inspection )<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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+2+ ALIGN=MIDDLE  ALT=\"+x+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Check the answers:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2Alog%284%2Cx%29+-+log%284%2C+3x+-+4%29+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+2%2Alog%284%2Cx%29+-+log%284%2C+3x+-+4%29+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2Alog%284%2C4%29+-+log%284%2C+3%2A4+-+4%29+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+2%2Alog%284%2C4%29+-+log%284%2C+3%2A4+-+4%29+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A1+-+log%28+4%2C+8+%29+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+2%2A1+-+log%28+4%2C+8+%29+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+4%2C8+%29+=+2+-+1%2F2+ ALIGN=MIDDLE  ALT=\"+log%28+4%2C8+%29+=+2+-+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+4%2C8+%29+=+3%2F2+ ALIGN=MIDDLE  ALT=\"+log%28+4%2C8+%29+=+3%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "This is true since<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%5E%283%2F2%29+=+8+ ALIGN=MIDDLE  ALT=\"+4%5E%283%2F2%29+=+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Square both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%5E3+=+64+ ALIGN=MIDDLE  ALT=\"+4%5E3+=+64+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+64+=+64+ ALIGN=MIDDLE  ALT=\"+64+=+64+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "You can check other solution\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );