document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012139>Question 1012139</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good evening to all<BR>\n" );
document.write( "I have some difficult to understand the difference between following <BR>\n" );
document.write( "two logarithmic equations<BR>\n" );
document.write( "a) log2(x^2 - 4x) =5    with solutions x=-4 V x=8<BR>\n" );
document.write( "b) log2(x) + log2(x-4) = 5 with only one solution x = 8<BR>\n" );
document.write( "As I know from log. properties the sum of 2 logarithms is the product of the<BR>\n" );
document.write( "arguments, so equation b) gives the product of arguments x^2 - 4x<BR>\n" );
document.write( "Where do I wrong?<BR>\n" );
document.write( "My thanks in advance <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627987 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=627987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log2(x) + log2(x-4) = 5<BR>\n" );
document.write( "log2 (x^2-4x)=5<BR>\n" );
document.write( "raise everything to the 2 power<BR>\n" );
document.write( "x^2-4x=32<BR>\n" );
document.write( "x^2-4x-32=0<BR>\n" );
document.write( "(x-8)(x+4)=0<BR>\n" );
document.write( "x=8, -4, but can't take a log of a negative number so there is only one solution.<BR>\n" );
document.write( "If the log is of (x^2-4x), then x=-4 works.<BR>\n" );
document.write( "As soon as you multiply the two together, you have slightly changed the form of the equation.  With quadratics and logs, it is necessary to put the root found back into the original equation to see if it works. Often, one does not. </SPAN>\n" );
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