document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129944>Question 129944</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving this logarithmic equation\r<BR>\n" );
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document.write( "log(x-14)-log5=log(x-12)-logx </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94888 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=94888\">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%2810%2C%28x-14%29%29-log%2810%2C%285%29%29=log%2810%2C%28x-12%29%29-log%2810%2C%28x%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28%28x-14%29%2F5%29%29=log%2810%2C%28%28x-12%29%2Fx%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%28%28x-14%29%2F5%29%29=log%2810%2C%28%28x-12%29%2Fx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the logs using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%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=%28x-14%29%2F5=%28x-12%29%2Fx ALIGN=MIDDLE  ALT=\"%28x-14%29%2F5=%28x-12%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise both sides as exponents with bases of 10 to eliminate the logs on both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%285%29x%28%28x-14%29%2Fcross%285%29%29=5cross%28x%29%28%28x-12%29%2Fcross%28x%29%29 ALIGN=MIDDLE  ALT=\"cross%285%29x%28%28x-14%29%2Fcross%285%29%29=5cross%28x%29%28%28x-12%29%2Fcross%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x ALIGN=MIDDLE  ALT=\"5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to eliminate the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-14%29=5%28x-12%29 ALIGN=MIDDLE  ALT=\"x%28x-14%29=5%28x-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-14x=5x-60 ALIGN=MIDDLE  ALT=\"x%5E2-14x=5x-60\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-14x-5x%2B60=0 ALIGN=MIDDLE  ALT=\"x%5E2-14x-5x%2B60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract 5x from both sides.  Add 60 to both sides. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-19x%2B60=0 ALIGN=MIDDLE  ALT=\"x%5E2-19x%2B60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-15%29%28x-4%29=0 ALIGN=MIDDLE  ALT=\"%28x-15%29%28x-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the left side (note: if you need help with factoring, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)\r<BR>\n" );
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document.write( "Now set each factor equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15 ALIGN=MIDDLE  ALT=\"x=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <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;\" >    Now solve for x in each case\r<BR>\n" );
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document.write( "So our possible answers are \r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15 ALIGN=MIDDLE  ALT=\"x=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <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;\" > \r<BR>\n" );
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document.write( "However, if you plug in <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;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28x-14%29%29-log%2810%2C%285%29%29=log%2810%2C%28x-12%29%29-log%2810%2C%28x%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > , you'll get a negative number inside the log. So our only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15 ALIGN=MIDDLE  ALT=\"x=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15 ALIGN=MIDDLE  ALT=\"x=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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