document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=314304>Question 314304</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble solving the following problems:\r<BR>\n" );
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document.write( "ln(sqrt(x-8)) = 5\r<BR>\n" );
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document.write( "log4x-log(12+(sqrt x)) = 2\r<BR>\n" );
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document.write( "The number N of trees of a given species per acre is approximated by the model N=68(10^-0.04x), 5 < x < 40, where x is the average diameter of the trees in inches 3 feet above the ground.  Use the model to approximate the average diameter of the trees in a test plot when N=21.\r<BR>\n" );
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document.write( "Someone please help!! I cannot figure them out and would GREATLY APPRECIATE IT!!\r<BR>\n" );
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document.write( "THANK YOU!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #224699 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=224699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ln(sqrt(x-8)) = 5<BR>\n" );
document.write( "sqrt(x-8) = e^5<BR>\n" );
document.write( "(x-8) = [e^10]<BR>\n" );
document.write( "x = e^10+8<BR>\n" );
document.write( "x = 22034<BR>\n" );
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document.write( "log4x-log(12+(sqrt x)) = 2<BR>\n" );
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document.write( "log[4x/[12+sqrt(x)] = 2<BR>\n" );
document.write( "4x/[12+sqrt(x)] = 10^2<BR>\n" );
document.write( "4x = 1200 + 100sqrt(x)<BR>\n" );
document.write( "x = 300 + sqrt(x)<BR>\n" );
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document.write( "x - sqrt(x) - 300 = 0<BR>\n" );
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document.write( "Let w = sqrt(x)<BR>\n" );
document.write( "Substitute to get:<BR>\n" );
document.write( "w^2 - w - 300 = 0<BR>\n" );
document.write( "w = [1 +- sqrt(1 - 4*-300)]/2<BR>\n" );
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document.write( "Positive solution:<BR>\n" );
document.write( "w = [1 + sqrt(1201)]/2 is approximately 17.8277<BR>\n" );
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document.write( "So, sqrt(x) = 17.8277<BR>\n" );
document.write( "x = 317.83<BR>\n" );
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document.write( "The number N of trees of a given species per acre is approximated by the model N=68(10^-0.04x), 5 < x < 40, where x is the average diameter of the trees in inches 3 feet above the ground. Use the model to approximate the average diameter of the trees in a test plot when N=21. <BR>\n" );
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document.write( "N=68(10^-0.04x)<BR>\n" );
document.write( "21 = 68(10^(-0.04x)<BR>\n" );
document.write( "0.3088 = 10^(-0.04x)<BR>\n" );
document.write( "Take the log of both sides to get:<BR>\n" );
document.write( "-0.04x = log(0.3088)<BR>\n" );
document.write( "x = 12.76 inches<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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