document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=243077>Question 243077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve the following problem.<BR>\n" );
document.write( "At what point(s) do the graphs of y=2log(x) and y=log(2x) intersect? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #178099 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=178099\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At what point(s) do the graphs of y=2log(x) and y=log(2x) intersect?<BR>\n" );
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document.write( "Substitute to get:<BR>\n" );
document.write( "2log(x) = log(2x)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "log(x^2) = log 2x<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "x^2 = 2x <BR>\n" );
document.write( "x^2-2x = 0<BR>\n" );
document.write( "x(x-2) = 0<BR>\n" );
document.write( "x = 0 or x=2<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "x cannot be zero because log(2*0) = log(0) does not exist.<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "So, x = 2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Then y = log(2x) = log(4) = 0.6021<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Point of intersection: (2,0.6021)<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );