document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173045>Question 173045</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please explain how to work this problem:  <BR>\n" );
document.write( "log of(x+1), base 2 plus 2 times the log of(x-1), base 4 equals 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127901 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=127901\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i think i have a solution for you.<BR>\n" );
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document.write( "before i go any further, your answer is:<BR>\n" );
document.write( "x = 3<BR>\n" );
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document.write( "i checked that out in the original formulas and it works.<BR>\n" );
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document.write( "the problem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28x%2B1%29%29+%2B+2%2Alog%284%2C%28x-1%29%29+=+3 ALIGN=MIDDLE  ALT=\"log%282%2C%28x%2B1%29%29+%2B+2%2Alog%284%2C%28x-1%29%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "so i could see the problem a little easier, i let:<BR>\n" );
document.write( "a = (x+1)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "b = (x-1)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the problem then looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Ca%29+%2B+2%2Alog%284%2Cb%29+=+3 ALIGN=MIDDLE  ALT=\"log%282%2Ca%29+%2B+2%2Alog%284%2Cb%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "i then wanted to get a common base, so i converted the logarithm with a base of 4 to a logarithm with a base of 2 using the conversion formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2Cb%29+=+log%282%2Cb%29%2Flog%282%2C4%29 ALIGN=MIDDLE  ALT=\"log%284%2Cb%29+=+log%282%2Cb%29%2Flog%282%2C4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the problem then looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Ca%29+%2B+2+%2A+%28log%282%2Cb%29%2Flog%282%2C4%29%29+=+3 ALIGN=MIDDLE  ALT=\"log%282%2Ca%29+%2B+2+%2A+%28log%282%2Cb%29%2Flog%282%2C4%29%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C4%29+=+d ALIGN=MIDDLE  ALT=\"log%282%2C4%29+=+d\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ed+=+4 ALIGN=MIDDLE  ALT=\"2%5Ed+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and i can show that d has to be equal to 2, then:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C4%29+=+2 ALIGN=MIDDLE  ALT=\"log%282%2C4%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the problem now looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Ca%29+%2B+2%2A%28log%282%2Cb%29%2F2%29+=+3 ALIGN=MIDDLE  ALT=\"log%282%2Ca%29+%2B+2%2A%28log%282%2Cb%29%2F2%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "this simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Ca%29+%2B+log%282%2Cb%29+=+3 ALIGN=MIDDLE  ALT=\"log%282%2Ca%29+%2B+log%282%2Cb%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since the laws of logarithms state:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Ca%2Ab%29+=+log%282%2Ca%29+%2B+log%282%2Cb%29 ALIGN=MIDDLE  ALT=\"log%282%2Ca%2Ab%29+=+log%282%2Ca%29+%2B+log%282%2Cb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "then:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Ca%29+%2B+log%282%2Cb%29 ALIGN=MIDDLE  ALT=\"log%282%2Ca%29+%2B+log%282%2Cb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > must equal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Ca%2Ab%29 ALIGN=MIDDLE  ALT=\"log%282%2Ca%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the problem now looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Ca%2Ab%29+=+3 ALIGN=MIDDLE  ALT=\"log%282%2Ca%2Ab%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the basic laws of logarithms state:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Ca%2Ab%29+=+3 ALIGN=MIDDLE  ALT=\"log%282%2Ca%2Ab%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E3+=+a%2Ab ALIGN=MIDDLE  ALT=\"2%5E3+=+a%2Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E3 ALIGN=MIDDLE  ALT=\"2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 8, the problem now looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ab+=+8 ALIGN=MIDDLE  ALT=\"a%2Ab+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if you recall from way back, i let:<BR>\n" );
document.write( "a = (x+1)<BR>\n" );
document.write( "b = (x-1)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "i can now substitute (x+1) for a, and (x-1) for b, and the problem now looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%2A%28x-1%29+=+8 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%2A%28x-1%29+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiplying out the factors, this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-1+=+8 ALIGN=MIDDLE  ALT=\"x%5E2+-1+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add 1 to both sides of the equation to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+9 ALIGN=MIDDLE  ALT=\"x%5E2+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "take the square root of both sides of the equation to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3 ALIGN=MIDDLE  ALT=\"x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "that's your answer.<BR>\n" );
document.write( "it was not a simple problem.<BR>\n" );
document.write( "you needed to be able to convert bases:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2Cb%29+=+log%282%2Cb%29%2Flog%282%2C4%29 ALIGN=MIDDLE  ALT=\"log%284%2Cb%29+=+log%282%2Cb%29%2Flog%282%2C4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you also needed to remember: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Ca%29+%2B+log%282%2Cb%29+=+log%282%2Ca%2Ab%29 ALIGN=MIDDLE  ALT=\"log%282%2Ca%29+%2B+log%282%2Cb%29+=+log%282%2Ca%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "fyi:<BR>\n" );
document.write( "you could have solved <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C4%29 ALIGN=MIDDLE  ALT=\"log%282%2C4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by converting to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C4%29%2Flog%2810%2C2%29 ALIGN=MIDDLE  ALT=\"log%2810%2C4%29%2Flog%2810%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as well as the way i showed you above.  then you could have used the log function of the calculator to get your answer.<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );