document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208905>Question 208905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation for x. \r<BR>\n" );
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document.write( "e^(ax) = Ce^(bx), where a is not equal to b </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157960 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=157960\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the equation for x. \r<BR>\n" );
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document.write( "e^(ax) = Ce^(bx), where a is not equal to b<BR>\n" );
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document.write( "Applying \"log rules\":<BR>\n" );
document.write( "e^(ax) = Ce^(bx)<BR>\n" );
document.write( "Divide both sides by e^(bx):<BR>\n" );
document.write( "e^(ax)/e^(bx) = C<BR>\n" );
document.write( "Rewriting the left side:<BR>\n" );
document.write( "e^(ax-bx) = C<BR>\n" );
document.write( "Take the ln of both sides:<BR>\n" );
document.write( "ax-bx = ln(C)<BR>\n" );
document.write( "Factor the left:<BR>\n" );
document.write( "x(a-b) = ln(C)<BR>\n" );
document.write( "Dividing we get:<BR>\n" );
document.write( "x = ln(C)/(a-b)<BR>\n" );
document.write( " </SPAN>\n" );
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