document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80458>Question 80458</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0495105104/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation: 1n x = 1n 2 + 1n (3x - 1)<BR>\n" );
document.write( "I know the answer is 2/5 from the answers in the back of the book. <BR>\n" );
document.write( "I need to know how the solution was solved. \r<BR>\n" );
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document.write( "I really appreciate your help.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57763 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=57763\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "1n <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1n <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 1n <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x+-+1%29 ALIGN=MIDDLE  ALT=\"%283x+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Collect the logarithms that contain x on one side of the equation.  You can do that by<BR>\n" );
document.write( "subtracting ln <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x+-+1%29 ALIGN=MIDDLE  ALT=\"%283x+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides of the equation.  When you do that subtraction<BR>\n" );
document.write( "you get:<BR>\n" );
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document.write( "ln <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > - ln <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x+-+1%29 ALIGN=MIDDLE  ALT=\"%283x+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = ln <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now apply the rule that the difference in two logarithms is the same as the log of their division.<BR>\n" );
document.write( "In equation form that rule says:<BR>\n" );
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document.write( "ln <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > - ln <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > = ln <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Fb%29 ALIGN=MIDDLE  ALT=\"%28a%2Fb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "With that rule the equation becomes:<BR>\n" );
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document.write( "ln <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%283x+-+1%29 ALIGN=MIDDLE  ALT=\"x%2F%283x+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = ln <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Look at this carefully ... comparing the left side to the right side.  For this to be<BR>\n" );
document.write( "true the two logarithms must be equal, and this means that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%283x+-+1%29+=+2 ALIGN=MIDDLE  ALT=\"x%2F%283x+-+1%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To get rid of the denominator, multiply both sides by the denominator of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-1 ALIGN=MIDDLE  ALT=\"3x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to<BR>\n" );
document.write( "get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-1%29%2A%28x%2F%283x-1%29%29+=+2%2A%283x+-+1%29 ALIGN=MIDDLE  ALT=\"%283x-1%29%2A%28x%2F%283x-1%29%29+=+2%2A%283x+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the left side the multiplier cancels with the denominator. And multiplying the right<BR>\n" );
document.write( "side, gives:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%283x-1%29%2A%28x%2Fcross%283x-1%29%29+=+6x+-+2 ALIGN=MIDDLE  ALT=\"cross%283x-1%29%2A%28x%2Fcross%283x-1%29%29+=+6x+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and it reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6x+-+2 ALIGN=MIDDLE  ALT=\"x+=+6x+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve this as you would any equation.  You need to gather all the terms that contain x <BR>\n" );
document.write( "on one side of the equation and everything else on the other side.  You can do this by<BR>\n" );
document.write( "subtracting 6x from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+6x+=+-2 ALIGN=MIDDLE  ALT=\"+x+-+6x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "combine the terms on the left side and the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x+=+-2 ALIGN=MIDDLE  ALT=\"-5x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "solve for x by dividing both sides by -5 and the outcome is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2%2F-5+=+2%2F5 ALIGN=MIDDLE  ALT=\"x+=+-2%2F-5+=+2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and that's how to get the book answer.  Hope this helps to familiarize you with logarithms. </SPAN>\n" );
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