document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=617078>Question 617078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me   \r<BR>\n" );
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document.write( "Solve for all values of x, to the nearest 10th.<BR>\n" );
document.write( "log4(2x&#8722;7)+log4(3x&#8722;3)=4	 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #388107 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=388107\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assuming these are base 4 logarithms...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C+%282x-7%29%29%2Blog%284%2C+%283x-3%29%29=4 ALIGN=MIDDLE  ALT=\"log%284%2C+%282x-7%29%29%2Blog%284%2C+%283x-3%29%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We want the equation in the form<BR>\n" );
document.write( "log(expression) = other-expression<BR>\n" );
document.write( "So we will use a property of logarithms, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%28p%29%29%2Blog%28a%2C+%28q%29%29+=+log%284%2C+%28p%2Aq%29%29 ALIGN=MIDDLE  ALT=\"log%28a%2C+%28p%29%29%2Blog%28a%2C+%28q%29%29+=+log%284%2C+%28p%2Aq%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to combine the logarithms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C+%28%282x-7%29%283x-3%29%29%29=4 ALIGN=MIDDLE  ALT=\"log%284%2C+%28%282x-7%29%283x-3%29%29%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now that the equation is in the desired form, the next step is to rewrite the equation in exponential form. In general <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%28p%29%29+=+q ALIGN=MIDDLE  ALT=\"log%28a%2C+%28p%29%29+=+q\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Eq+=+p ALIGN=MIDDLE  ALT=\"a%5Eq+=+p\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Using this pattern on our equation we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E4+=+%282x-7%29%283x-3%29 ALIGN=MIDDLE  ALT=\"4%5E4+=+%282x-7%29%283x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=256+=+6x%5E2-27x%2B21 ALIGN=MIDDLE  ALT=\"256+=+6x%5E2-27x%2B21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now that the variable is out of the logarithm, we can solve for it. This is a quadratic equation so we want one side to be zero. Subtracting 256 from each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+6x%5E2-27x-235 ALIGN=MIDDLE  ALT=\"0+=+6x%5E2-27x-235\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next we factor or use the Quadratic Formula. This will not factor so we must use the formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-27%29+%2B-+sqrt%28%28-27%29%5E2+-+4%286%29%28-235%29%29%29%2F2%286%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-27%29+%2B-+sqrt%28%28-27%29%5E2+-+4%286%29%28-235%29%29%29%2F2%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-27%29+%2B-+sqrt%28729+-+4%286%29%28-235%29%29%29%2F2%286%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-27%29+%2B-+sqrt%28729+-+4%286%29%28-235%29%29%29%2F2%286%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-%28-27%29+%2B-+sqrt%28729+-+%28-5640%29%29%29%2F2%286%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-27%29+%2B-+sqrt%28729+-+%28-5640%29%29%29%2F2%286%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-%28-27%29+%2B-+sqrt%28729+-+%28-5640%29%29%29%2F2%286%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-27%29+%2B-+sqrt%28729+-+%28-5640%29%29%29%2F2%286%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-%28-27%29+%2B-+sqrt%286369%29%29%2F2%286%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-27%29+%2B-+sqrt%286369%29%29%2F2%286%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+=+%2827+%2B-+sqrt%286369%29%29%2F12 ALIGN=MIDDLE  ALT=\"x+=+%2827+%2B-+sqrt%286369%29%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2827+%2B+sqrt%286369%29%29%2F12 ALIGN=MIDDLE  ALT=\"x+=+%2827+%2B+sqrt%286369%29%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2827+-+sqrt%286369%29%29%2F12 ALIGN=MIDDLE  ALT=\"x+=+%2827+-+sqrt%286369%29%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Since you were asked for decimal answers, get out your calculator and round off your answer to the nearest tenth.\r<BR>\n" );
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