document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=110200>Question 110200</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help! Thanks tutors!\r<BR>\n" );
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document.write( "log2(x-1) - log2(x+3)= log2(1/x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80357 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=80357\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28x-1%29%29+-+log%282%2C%28x%2B3%29%29+=+log%282%2C%281%2Fx%29%29 ALIGN=MIDDLE  ALT=\"log%282%2C%28x-1%29%29+-+log%282%2C%28x%2B3%29%29+=+log%282%2C%281%2Fx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To solve for x, first recognize that the difference of the logs (to the same base) of two quantities <BR>\n" );
document.write( "is equal to the log of the division of the two quantities.<BR>\n" );
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document.write( "Using this rule of logarithms means you can convert:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28x-1%29%29+-+log%282%2C%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"log%282%2C%28x-1%29%29+-+log%282%2C%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28%28x-1%29%2F%28x%2B3%29%29%29 ALIGN=MIDDLE  ALT=\"log%282%2C%28%28x-1%29%2F%28x%2B3%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute this conversion into the equation and it becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28%28x-1%29%2F%28x%2B3%29%29%29+=+log%282%2C%281%2Fx%29%29 ALIGN=MIDDLE  ALT=\"log%282%2C%28%28x-1%29%2F%28x%2B3%29%29%29+=+log%282%2C%281%2Fx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Look carefully at this. For the left side to be equal to the right side, the two quantities undergoing<BR>\n" );
document.write( "the log operator must be equal. That means:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-1%29%2F%28x%2B3%29%29+=+1%2Fx ALIGN=MIDDLE  ALT=\"%28%28x-1%29%2F%28x%2B3%29%29+=+1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is a proportion and you can simplify proportions by cross multiplying ... multiplying<BR>\n" );
document.write( "the numerator by the denominator on the other side ... for both numerators.<BR>\n" );
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document.write( "When you do that you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%2Ax+=+1%2A%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%2Ax+=+1%2A%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply out both sides and this equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-x+=+x+%2B+3 ALIGN=MIDDLE  ALT=\"x%5E2+-x+=+x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the x on the right side by subtracting x 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%5E2+-+2x+=+3 ALIGN=MIDDLE  ALT=\"x%5E2+-+2x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then get rid of the 3 on the right side by subtracting 3 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%5E2+-+2x+-+3+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+2x+-+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The left side of this equation factors to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-3%29%2A%28x+%2B+1%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-3%29%2A%28x+%2B+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This equation will be true if either of the factors is zero ... which would cause a<BR>\n" );
document.write( "multiplication by zero on the left side and therefore make the left side become zero which equals<BR>\n" );
document.write( "the right side. Note that one of the factors will be zero if x = +3 or if x = -1.<BR>\n" );
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document.write( "Note however that if x equals -1, several of the terms on which the log function is operating<BR>\n" );
document.write( "will become negative, and the log of a negative number is not permitted. Therefore,<BR>\n" );
document.write( "x = +3 is the only valid answer.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and the steps you can go through to solve <BR>\n" );
document.write( "for x.<BR>\n" );
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