document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=744481>Question 744481</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Solve the following equations<BR>\n" );
document.write( "a) log x+1 = log 6 - log x<BR>\n" );
document.write( "b) ln(x-2) +ln3 = ln(x+1)\r<BR>\n" );
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document.write( "Can you please help me out? Thanks so much in advance:)<BR>\n" );
document.write( "Can you please show all the steps it would really help me understand:) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #453413 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=453413\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Solve the following equations<BR>\n" );
document.write( "a) log x+1 = log 6 - log x<BR>\n" );
document.write( "Subtracting logs means divide so we can combine on the right to<BR>\n" );
document.write( "log(x+1) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%286%2Fx%29%29 ALIGN=MIDDLE  ALT=\"log%28%286%2Fx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if the logs are equal, the values are equal, therefore:<BR>\n" );
document.write( "x + 1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fx ALIGN=MIDDLE  ALT=\"6%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply both sides by x<BR>\n" );
document.write( "x(x+1) = 6<BR>\n" );
document.write( "arrange as a quadratic equation<BR>\n" );
document.write( "x^2 + x - 6 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(x+3)(x-2)<BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "x = -3<BR>\n" );
document.write( "x = +2, this is the only solution, (we can't find the log of a neg number)<BR>\n" );
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document.write( "Check this on a calc:<BR>\n" );
document.write( " enter: log(2+1) results: .477..<BR>\n" );
document.write( " then<BR>\n" );
document.write( " enter: log(6) - log(2): results: .477..; equality confirms our solution of x=2<BR>\n" );
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document.write( "b) ln(x-2) + ln(3) = ln(x+1) <BR>\n" );
document.write( "Adding logs is multiply, combine on the left<BR>\n" );
document.write( "ln(3(x-2)) = ln(x+1)<BR>\n" );
document.write( "ln(3x-6) = ln(x+1)<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "3x - 6 = x + 1<BR>\n" );
document.write( "3x - x = 1 + 6<BR>\n" );
document.write( "2x = 7<BR>\n" );
document.write( "x = 7/2<BR>\n" );
document.write( "x = 3.5<BR>\n" );
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document.write( "Check this on a calc replace x with 3.5:<BR>\n" );
document.write( "enter: ln(3.5-2) + ln(3); results: 1.504..<BR>\n" );
document.write( "enter: ln(3.5+1); results: 1.504.. confirms our solution of x=3.5<BR>\n" );
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document.write( "Are you understanding this better now?  C<BR>\n" );
document.write( " </SPAN>\n" );
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