document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083333>Question 1083333</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Why x = 7 is not a solution to the equation:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28x%2B3%29%28x-8%29%29+%2B+log%2810%2C%28%28x%2B3%29%2F%28x-8%29%29%29+=+2 ALIGN=MIDDLE  ALT=\"log%2810%2C%28x%2B3%29%28x-8%29%29+%2B+log%2810%2C%28%28x%2B3%29%2F%28x-8%29%29%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697339 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=697339\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log((x+3)/(x-8)) would lead to the log of a negative number which is not allowed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i believe the equation is log((x+3)*(x-8)) + log((x+3)/(x-8)) = 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that makes more sense than having the (x-8) outside of the log function as you show it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i graphed it and found x to be equal to -13.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that value of x makes the equation true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i then proceeded to solve it algebraically and came up with the source of the problem.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's what i did:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "start with log((x+3)*(x-8)) + log((x+3)/(x-8)) = 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is equivalent to log(x+3) + log(x-8) + log(x+3) - log(x-8) = 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the plus and minus log(x-8) cancel out and you are left with:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "log(x+3) + log(x+3) = 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is equivalent to 2 * log(x+3) = 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i then divided both sides of the equation by 2 to get log(x+3) = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is true if and only if 10^1 = x+3 which results in x = 7.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that doesn't work because log((x+3)/(x-8)) becomes the log of a negative number which is not allowed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i then looked at it in a different way.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "starting from 2 * log(x+3)) = 2, i used the fact that 2 * log(x+3)) is equivalent to log((x+3)^2), so the equation became:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "log((x+3)^2) = 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is true if and only if 10^2 = (x+3)^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this becomes 100 = (x+3)^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "take the square root of both sides of the equation and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x+3) = plus or minus 10.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + 3 = 10 leads to x = 7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + 3 = -10 leads to x = -13\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "bingo !!!!!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = -13 is the answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this was confirmed graphically as shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/053101.jpg\" alt=\"###\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );