document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=40754>Question 40754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I desperately need help with these few questions.  This is a take home test that needs to be done by tommorow. <BR>\n" );
document.write( "1. The number of bacteria present in a culture is B=10e^1923t where t is the time in minutes.  Find the time required, to the nearest half minute, to have 3200 bacteria present.\r<BR>\n" );
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document.write( "12. log(5x-1)=2+log(x-2)<BR>\n" );
document.write( "13. log(x^3)=(logx)^2\r<BR>\n" );
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document.write( "Thank you Very Much,<BR>\n" );
document.write( "Art </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26133 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=26133\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. The number of bacteria present in a culture is B=10e^1923t where t is the time in minutes.  Find the time required, to the nearest half minute, to have 3200 bacteria present.<BR>\n" );
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document.write( "3200=10e^(1932t)<BR>\n" );
document.write( "320=e^(1932t)<BR>\n" );
document.write( "Take the natural log of both sides to get:<BR>\n" );
document.write( "ln(320)=1932t<BR>\n" );
document.write( "t=5.76832.../1932=0.00298567...<BR>\n" );
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document.write( "12. log(5x-1)=2+log(x-2)<BR>\n" );
document.write( "   log(5x-1)-log(x-2)=2<BR>\n" );
document.write( "   log[(5x-1)/(x-2)]=2<BR>\n" );
document.write( "       (5x-1)/(x-2)=10^2<BR>\n" );
document.write( "     5x-1=100(x-2)<BR>\n" );
document.write( "     5x-1-100x+200=0<BR>\n" );
document.write( "     -95x=-199<BR>\n" );
document.write( "      x=2.0947...<BR>\n" );
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document.write( "13. log(x^3)=(logx)^2<BR>\n" );
document.write( "    3logx =(logx)^2<BR>\n" );
document.write( "    (logx)^2-3logx=0<BR>\n" );
document.write( "Factor out the logx to get:<BR>\n" );
document.write( "   (logx)(logx-3)=0<BR>\n" );
document.write( "logx=0 or logx=3<BR>\n" );
document.write( "If logx=0 10^0=x. Therefore x=1<BR>\n" );
document.write( "If logx=3 10^3=x. Therefore x=1000<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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