document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=554012>Question 554012</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x:<BR>\n" );
document.write( "Log2(11-6x) = 2Log2(x-1)+3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #361158 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=361158\">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%282%2C%2811-6x%29%29+=+2log%282%2C%28x-1%29%29+%2B+3 ALIGN=MIDDLE  ALT=\"log%282%2C%2811-6x%29%29+=+2log%282%2C%28x-1%29%29+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First get all the log terms on one side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%2811-6x%29%29-2log%282%2C%28x-1%29%29+=+3 ALIGN=MIDDLE  ALT=\"log%282%2C%2811-6x%29%29-2log%282%2C%28x-1%29%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "By the Law of Logarithms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%2811-6x%29%29+-log%282%2C%28x-1%29%5E2%29+=+3 ALIGN=MIDDLE  ALT=\"log%282%2C%2811-6x%29%29+-log%282%2C%28x-1%29%5E2%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "By another Law of Logarithms, combine into a single log:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28%2811-6x%29%2F%28x-1%29%5E2%29%29+=+3 ALIGN=MIDDLE  ALT=\"log%282%2C%28%2811-6x%29%2F%28x-1%29%5E2%29%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "By the Definition of Logarithms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E3=+%2811-6x%29%2F%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"2%5E3=+%2811-6x%29%2F%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+=+%2811-6x%29%2F%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"8+=+%2811-6x%29%2F%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Clear the fraction, by multiplying both sides by (x-1)^2:\r<BR>\n" );
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document.write( "8(x-1)^2= 11-6x<BR>\n" );
document.write( "8(x^2-2x+1) =11-6x<BR>\n" );
document.write( "8x^2-16x+8+6x-11=0<BR>\n" );
document.write( "8x^2-10x-3=0\r<BR>\n" );
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document.write( "What are the chances that, after ALL this work, the trinomial will factor??  They usually do, in this type of problem!!\r<BR>\n" );
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document.write( "(4x +1)(2x-3)=0\r<BR>\n" );
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document.write( "There are two solutions:  x=-1/4 and x=3/2\r<BR>\n" );
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document.write( "Of course, you can't have a log of a negative number, so x=-1/4 must be rejected.  The other answer x=3/2 is acceptable.\r<BR>\n" );
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document.write( "You may want to see my FREE website for additional explanation on LOGARITHMS.  The easiest way to find the website is to use the easy-to-remember and easy-to-spell link www.mathinlivingcolor.com.  Near the bottom of this page is a link that takes you to my Homepage.  On my Homepage, look for the link \"Basic, Intermediate, and College Algebra: One Step at a Time.\"  \r<BR>\n" );
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document.write( "Choose \"College Algebra\" and look in Chapter 4 for the sections on Logarithms.  I think you will really like the \"Math in Living Color\" pages that go with these sections.  In addition, I have 2 FREE videos on this topic that was made in my younger years before I retired.  To see the videos, look on my Homepage for the link \"Rapalje Videos in Living Color.\"  Choose College Algebra, and look for the videos on \"Logarithms.\"\r<BR>\n" );
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document.write( "If you need to contact me, send me an Email at rapaljer@seminolestate.edu.\r<BR>\n" );
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document.write( "Dr. Robert J. Rapalje, Retired<BR>\n" );
document.write( "Seminole State College of Florida<BR>\n" );
document.write( "Altamonte Springs Campus </SPAN>\n" );
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