document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135088>Question 1135088</A>: <I><SPAN STYLE=\"word-break: break-all;\"> logbase4logx(base2) + logbase2logx(base4) = 2. Find x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752634 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=752634\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C%28log%282%2Cx%29%29%29+%2B+log%282%2C%28log%284%2Cx%29%29%29+=+2 ALIGN=MIDDLE  ALT=\"log%284%2C%28log%282%2Cx%29%29%29+%2B+log%282%2C%28log%284%2Cx%29%29%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Apply log rule : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%28a%2Cb+%29=+log%28c%2Cb+%29%2Flog+%28c%2Ca+%29 ALIGN=MIDDLE  ALT=\"log+%28a%2Cb+%29=+log%28c%2Cb+%29%2Flog+%28c%2Ca+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28log%284%2Cx%29%29%29=log%284%2C%28log%284%2Cx%29%29%29%2Flog%284%2C2%29 ALIGN=MIDDLE  ALT=\"log%282%2C%28log%284%2Cx%29%29%29=log%284%2C%28log%284%2Cx%29%29%29%2Flog%284%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C%28log%282%2Cx%29%29%29+%2Blog%284%2C%28log%284%2Cx%29%29%29%2Flog%284%2C2%29=2 ALIGN=MIDDLE  ALT=\"log%284%2C%28log%282%2Cx%29%29%29+%2Blog%284%2C%28log%284%2Cx%29%29%29%2Flog%284%2C2%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >....simplify\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C%28log%284%2Cx%29%29%29%2Flog%284%2C2%29=2log%284%2C%28log%284%2Cx%29%29%29 ALIGN=MIDDLE  ALT=\"log%284%2C%28log%284%2Cx%29%29%29%2Flog%284%2C2%29=2log%284%2C%28log%284%2Cx%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, you have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C%28log%282%2Cx%29%29%29+%2B2log%284%2C%28log%284%2Cx%29%29%29=2 ALIGN=MIDDLE  ALT=\"log%284%2C%28log%282%2Cx%29%29%29+%2B2log%284%2C%28log%284%2Cx%29%29%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C%28log%282%2Cx%29%29%29+%2Blog%284%2C%28log%284%2Cx%29%29%5E2%29=2 ALIGN=MIDDLE  ALT=\"log%284%2C%28log%282%2Cx%29%29%29+%2Blog%284%2C%28log%284%2Cx%29%29%5E2%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Apply log rule : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28c%2Ca+%29%2Blog%28c%2Cb+%29=log%28c%2C%28ab%29%29 ALIGN=MIDDLE  ALT=\"log%28c%2Ca+%29%2Blog%28c%2Cb+%29=log%28c%2C%28ab%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C%28log%282%2Cx%29%29%2A%28log%284%2Cx%29%29%5E2%29=2 ALIGN=MIDDLE  ALT=\"log%284%2C%28log%282%2Cx%29%29%2A%28log%284%2Cx%29%29%5E2%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Apply log rule : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=log%28b%2Cb%5Ea%29 ALIGN=MIDDLE  ALT=\"a=log%28b%2Cb%5Ea%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=log%284%2C4%5E2%29=log%284%2C16+%29 ALIGN=MIDDLE  ALT=\"2=log%284%2C4%5E2%29=log%284%2C16+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C%28log%282%2Cx%29%29%2A%28log%284%2Cx%29%29%5E2%29=log%284%2C16+%29 ALIGN=MIDDLE  ALT=\"log%284%2C%28log%282%2Cx%29%29%2A%28log%284%2Cx%29%29%5E2%29=log%284%2C16+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "When the logs have the same base: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%28b%2Cf%28x%29%29=log%28b%2Cg%28x%29%29 ALIGN=MIDDLE  ALT=\"log+%28b%2Cf%28x%29%29=log%28b%2Cg%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=g%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29=g%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%29%2A%28log%284%2Cx%29%29%5E2=16+ ALIGN=MIDDLE  ALT=\"log%282%2Cx%29%2A%28log%284%2Cx%29%29%5E2=16+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%282%2Cx%29 ALIGN=MIDDLE  ALT=\"log+%282%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%284%2Cx%29%2Flog%284%2C2%29 ALIGN=MIDDLE  ALT=\"log+%284%2Cx%29%2Flog%284%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log+%284%2Cx%29%2Flog%284%2C2%29%29%2A%28log%284%2Cx%29%29%5E2=16+ ALIGN=MIDDLE  ALT=\"%28log+%284%2Cx%29%2Flog%284%2C2%29%29%2A%28log%284%2Cx%29%29%5E2=16+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log+%284%2Cx%29%29%5E3%2Flog%284%2C2%29=16+ ALIGN=MIDDLE  ALT=\"%28log+%284%2Cx%29%29%5E3%2Flog%284%2C2%29=16+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log+%284%2Cx%29%29%5E3%2F%281%2F2%29=16+ ALIGN=MIDDLE  ALT=\"%28log+%284%2Cx%29%29%5E3%2F%281%2F2%29=16+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28log+%284%2Cx%29%29%5E3=16+ ALIGN=MIDDLE  ALT=\"2%28log+%284%2Cx%29%29%5E3=16+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log+%284%2Cx%29%29%5E3=8+ ALIGN=MIDDLE  ALT=\"%28log+%284%2Cx%29%29%5E3=8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28g+%28x+%29+%29%5En=f+%28a+%29 ALIGN=MIDDLE  ALT=\"%28g+%28x+%29+%29%5En=f+%28a+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > when<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > is odd, the solution is :<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=root%28n%2Cf%28a%29%29 ALIGN=MIDDLE  ALT=\"g%28x%29=root%28n%2Cf%28a%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%284%2Cx%29=root%283%2C8%29+ ALIGN=MIDDLE  ALT=\"log+%284%2Cx%29=root%283%2C8%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=log+%284%2Cx%29=2+ ALIGN=MIDDLE  ALT=\"log+%284%2Cx%29=2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >....change to base <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%28x%29%2Flog+%284%29=2+ ALIGN=MIDDLE  ALT=\"log+%28x%29%2Flog+%284%29=2+\"   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=log+%28x%29=2log+%284%29+ ALIGN=MIDDLE  ALT=\"log+%28x%29=2log+%284%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%28x%29=log+%284%5E2%29+ ALIGN=MIDDLE  ALT=\"log+%28x%29=log+%284%5E2%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=log+%28x%29=log+%2816%29+ ALIGN=MIDDLE  ALT=\"log+%28x%29=log+%2816%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...if log same,=>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=16 ALIGN=MIDDLE  ALT=\"x=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );