document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=991937>Question 991937</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help in solving the equation for x : ln&#8289;&#12310;5x^2 &#12311;- ln&#8289;x = 3<BR>\n" );
document.write( "a) 0.22 <BR>\n" );
document.write( "b) 0.60 <BR>\n" );
document.write( "c) 1.59 <BR>\n" );
document.write( "d) 4.02<BR>\n" );
document.write( "Would very much appreciate if workings can be shown, thank you.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #611631 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=611631\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> answer is d (4.02).\r<BR>\n" );
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document.write( "here's why:\r<BR>\n" );
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document.write( "ln(5x^2) - ln(x) = 3\r<BR>\n" );
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document.write( "since ln(a) - ln(b) = ln(a/b), you get:\r<BR>\n" );
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document.write( "ln(5x^2) - ln(x) = 3 becomes:\r<BR>\n" );
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document.write( "ln(5x^2/x) = 3\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "ln(5x) = 3\r<BR>\n" );
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document.write( "this is true if and only if e^3 = 5x\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = e^3 / 5\r<BR>\n" );
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document.write( "evaluate to get:\r<BR>\n" );
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document.write( "x = 4.017107385 which rounds to 4.02.\r<BR>\n" );
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document.write( "confirm your solution is correct by replacing x with 4.017107385 in your original equation and you will see that the equation is true.\r<BR>\n" );
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