document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=585261>Question 585261</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (Solving Natural Logarithms to solve Exponential Equations)Give an exact answer and then an answer rounded to the nearest thousandth.\r<BR>\n" );
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document.write( "Problem:\r<BR>\n" );
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document.write( "3^x-1=4^2x+3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #373275 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=373275\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3^(x-1)=4^(2x+3)<BR>\n" );
document.write( "take ln of both sides:<BR>\n" );
document.write( "ln(3^(x-1)) = ln(4^(2x+3))<BR>\n" );
document.write( "(x-1)ln(3) = (2x+3)ln(4)<BR>\n" );
document.write( "xln(3)-ln(3) = (2x)ln(4)+3ln(4)<BR>\n" );
document.write( "xln(3) = (2x)ln(4)+3ln(4)+ln(3)<BR>\n" );
document.write( "xln(3)-(2x)ln(4) = 3ln(4)+ln(3)<BR>\n" );
document.write( "x(ln(3)-(2)ln(4)) = 3ln(4)+ln(3)<BR>\n" );
document.write( "x = (3ln(4)+ln(3))/(ln(3)-(2)ln(4))  exact<BR>\n" );
document.write( "x = -3.141\r<BR>\n" );
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document.write( " </SPAN>\n" );
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