document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76241>Question 76241</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618250204/algebrahomeworkh>algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> ln x+ln9x-20=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54706 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=54706\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ln(x) + ln(9x) - 20 = 1<BR>\n" );
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document.write( "Adding logarithms is the same as multiplying.  So ln(x) + ln(9x) is the same as ln(x*9x)<BR>\n" );
document.write( "and multiplying x*9x results in 9x^2.  So now the equation is:<BR>\n" );
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document.write( "ln(9x^2) - 20 = 1<BR>\n" );
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document.write( "Now add 20 to both sides and you get:<BR>\n" );
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document.write( "ln(9x^2) = 21<BR>\n" );
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document.write( "by switching to the exponential form this can be transformed to:<BR>\n" );
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document.write( "e^21 = 9x^2<BR>\n" );
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document.write( "Divide both sides by 9 and transpose to get:<BR>\n" );
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document.write( "x^2 = (e^21)/9 <BR>\n" );
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document.write( "Now use a calculator to find that e^21 = 1318815734 and then dividing that by 9 you get<BR>\n" );
document.write( "146535081.6<BR>\n" );
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document.write( "Substituting this for the right side of the equation results in:<BR>\n" );
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document.write( "x^2 = 146535081.6 <BR>\n" );
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document.write( "Taking the square root of both sides results in x = 12105.16756<BR>\n" );
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document.write( "Check this out by substituting this value for x into the original problem.  You get:<BR>\n" );
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document.write( "ln(12105.16756) + ln(9*12105.16756) - 20 = 1<BR>\n" );
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document.write( "Using a calculator you will find that ln(12105.16756) = 9.401387711 and ln(9*12105.16756)<BR>\n" );
document.write( "is ln(108946.508) and your calculator will convert this to 11.59861229.  Substituting<BR>\n" );
document.write( "this into the equation results in:<BR>\n" );
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document.write( "9.401387711 + 11.59861229 - 20 = 1<BR>\n" );
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document.write( "The sum of the first two terms is 21.  Substituting 21 in place of the two terms gives:<BR>\n" );
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document.write( "21 - 20 = 1<BR>\n" );
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document.write( "This equation balances which tells us that x does equal 12105.16756<BR>\n" );
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document.write( "Hope this helps you by providing one way to get a solution to this problem. </SPAN>\n" );
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