document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1032611>Question 1032611</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each equation for x.<BR>\n" );
document.write( "(a) 30 = 80(1 &#8722; e^&#8722;2x)<BR>\n" );
document.write( "(b) 5 X 2^x = 3^ (x&#8722;1) ; ( here capital X is for multiply ) <BR>\n" );
document.write( "(c) log2(log3 x) = 5 ; ( here 2 and 3 are bases of the logs ) <BR>\n" );
document.write( "(d) e^&#8722; 1/2log(x^2 &#8722; 1) =1/ sqrt 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #647273 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=647273\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve each equation for x.<BR>\n" );
document.write( "(a) 30 = 80(1 &#8722; e^&#8722;2x)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "1-e^(-2x) = 3/8<BR>\n" );
document.write( "e^(-2x) = 5/8<BR>\n" );
document.write( "-2x = ln(5/8)<BR>\n" );
document.write( "-2x = -0.47<BR>\n" );
document.write( "x = 0.235<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "----<BR>\n" );
document.write( "(b) 5 X 2^x = 3^ (x&#8722;1) ; ( here capital X is for multiply )<BR>\n" );
document.write( "log(5) + x*log(2) = (x-1)log(3)<BR>\n" );
document.write( "------<BR>\n" );
document.write( "log(5) + x*log(2) = x*log(3) - log(3)<BR>\n" );
document.write( "x(log(2)-log(3)) = -[log(3)+log(5)] <BR>\n" );
document.write( "x = -[log(3)+log(5)]/[log(2)-log(3)]I'll leave the arithmetic to you.<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "(c) log2(lo3 x) = 5 ; ( here 2 and 3 are bases of the logs )<BR>\n" );
document.write( "log2[log(x)/log(3)] = 5<BR>\n" );
document.write( "---<BR>\n" );
document.write( "log2[log(x)] - log2[log(3)] = 5<BR>\n" );
document.write( "---<BR>\n" );
document.write( "log2[log(x)] - log2[0.4771] = 5<BR>\n" );
document.write( "log2[log(x)] - log(0.4771)/log(2) = 5<BR>\n" );
document.write( "log2[log(x)] + 1.0676 = 5<BR>\n" );
document.write( "log2[log(x)] = 3.9324<BR>\n" );
document.write( "log(x) = 2^3.9324 = 15.2672<BR>\n" );
document.write( "x = 10^15.2672 = 1.85..x10^15<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "(d) e^&#8722; 1/2*log(x^2 &#8722; 1) =1/ sqrt 3<BR>\n" );
document.write( "0.6065*log(x^2-1) = 0.5774<BR>\n" );
document.write( "log(x^2-1) = 0.9519<BR>\n" );
document.write( "x^2-1 = 10^0.9519 = 8.9523<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x^2 = 9.9523<BR>\n" );
document.write( "x = 3.1547<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );