document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=278787>Question 278787</A>: <I><SPAN STYLE=\"word-break: break-all;\"> log3 (2x – 1) – log3 (x – 4) = 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #202797 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=202797\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equations reads like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%282x-1%29%29+-+log%283%2C%28x-4%29%29+=+2 ALIGN=MIDDLE  ALT=\"log%283%2C%282x-1%29%29+-+log%283%2C%28x-4%29%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%2Fy%29+=+log%28x%29+-+log%28y%29 ALIGN=MIDDLE  ALT=\"log%28x%2Fy%29+=+log%28x%29+-+log%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, your equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%28%282x-1%29%2F%28x-4%29%29%29+=+2 ALIGN=MIDDLE  ALT=\"log%283%2C%28%282x-1%29%2F%28x-4%29%29%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The basic definition of logarithms states that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%28b%2Cx%29 ALIGN=MIDDLE  ALT=\"y+=+log%28b%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Ey+=+x ALIGN=MIDDLE  ALT=\"b%5Ey+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "by the basic definition of logarithms, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%28%282x-1%29%2F%28x-4%29%29%29+=+2 ALIGN=MIDDLE  ALT=\"log%283%2C%28%282x-1%29%2F%28x-4%29%29%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2+=+%282x-1%29%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"3%5E2+=+%282x-1%29%2F%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "9 = (2x-1)/(x-4)\r<BR>\n" );
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document.write( "multiply both sides of this equation by (x-4) to get:\r<BR>\n" );
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document.write( "9*(x-4) = (2x-1)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "9x - 36 = 2x - 1\r<BR>\n" );
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document.write( "subtract 2x from both sides of this equation and add 36 to both sides of this equation to get:\r<BR>\n" );
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document.write( "9x - 2x = -1 + 36\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "7x = 35\r<BR>\n" );
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document.write( "divide both sides of this equation by 7 to get:\r<BR>\n" );
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document.write( "x = 5\r<BR>\n" );
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document.write( "your answer should be x = 5.\r<BR>\n" );
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document.write( "substitute in your original equation to see if this is true.\r<BR>\n" );
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document.write( "your original equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%282x-1%29%29+-+log%283%2C%28x-4%29%29+=+2 ALIGN=MIDDLE  ALT=\"log%283%2C%282x-1%29%29+-+log%283%2C%28x-4%29%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "substitute 5 for x to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%282%2A5-1%29%29+-+log%283%2C%285-4%29%29+=+2 ALIGN=MIDDLE  ALT=\"log%283%2C%282%2A5-1%29%29+-+log%283%2C%285-4%29%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C9%29+-+log%283%2C1%29+=+2 ALIGN=MIDDLE  ALT=\"log%283%2C9%29+-+log%283%2C1%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%289%2F1%29%29+=+2 ALIGN=MIDDLE  ALT=\"log%283%2C%289%2F1%29%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C9%29 ALIGN=MIDDLE  ALT=\"log%283%2C9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2 which is true if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2+=+9 ALIGN=MIDDLE  ALT=\"3%5E2+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > which it is.\r<BR>\n" );
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document.write( "your answer is:\r<BR>\n" );
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document.write( "x = 5\r<BR>\n" );
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document.write( " </SPAN>\n" );
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