document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=863604>Question 863604</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to solve 2log(x+1) - log (x+3) = log1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #520486 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=520486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rules of log that apply (rule numbers are mine created for this problem only):<BR>\n" );
document.write( "rule 1:<BR>\n" );
document.write( "a*log(b) = log(b^a)<BR>\n" );
document.write( "rule 2:<BR>\n" );
document.write( "log(a) - log(b) = log(a/b)<BR>\n" );
document.write( "rule 3:<BR>\n" );
document.write( "if log(a) = log(b) then a = b<BR>\n" );
document.write( "rule 4:<BR>\n" );
document.write( "you cannot take the log of a negative number\r<BR>\n" );
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document.write( "original problem:<BR>\n" );
document.write( "2log(x+1) - log(x+3) = log(1)<BR>\n" );
document.write( "apply rule 1 to get:<BR>\n" );
document.write( "log((x+1)^2) - log(x+3) = log(1)<BR>\n" );
document.write( "apply rule 2 to get:<BR>\n" );
document.write( "log((x+1)^2)/(x+3)) = log(1)<BR>\n" );
document.write( "apply rule 3 to get:<BR>\n" );
document.write( "(x+1)^2/(x+3) = 1<BR>\n" );
document.write( "multiply both sides of this equation by (x+3) to get:<BR>\n" );
document.write( "(x+1)^2 = (x+3)<BR>\n" );
document.write( "subtract (x+3) from both sides of this equation to get:<BR>\n" );
document.write( "(x+1)^2 - (x+3) = 0<BR>\n" );
document.write( "simplify by performing indicated operations to get:<BR>\n" );
document.write( "x^2 + 2x + 1 - x - 3 = 0<BR>\n" );
document.write( "simplify by combining like terms to get:<BR>\n" );
document.write( "x^2 + x - 2 = 0<BR>\n" );
document.write( "factor to get:<BR>\n" );
document.write( "(x+2) * (x-1) = 0<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = -2<BR>\n" );
document.write( "x = 1<BR>\n" );
document.write( "apply rule 4 to reject x = -2 as a valid answer because 2log(x+1) becomes 2log(-1).\r<BR>\n" );
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document.write( "your solution is x = 1.<BR>\n" );
document.write( "substitute for x in the original equation to confirm this solution is good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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