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" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627989 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39630)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=627989\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28x%5E2-4x%29%29=5 ALIGN=MIDDLE  ALT=\"log%282%2C%28x%5E2-4x%29%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28x%28x-4%29%29%29=5 ALIGN=MIDDLE  ALT=\"log%282%2C%28x%28x-4%29%29%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >----correct but unnecessary<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E5=x%5E2-4x ALIGN=MIDDLE  ALT=\"2%5E5=x%5E2-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x-2%5E5=0 ALIGN=MIDDLE  ALT=\"x%5E2-4x-2%5E5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x-32=0 ALIGN=MIDDLE  ALT=\"x%5E2-4x-32=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----quadratic equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x-8%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x-8%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(b)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%29%2Blog%282%2C%28x-4%29%29=5 ALIGN=MIDDLE  ALT=\"log%282%2Cx%29%2Blog%282%2C%28x-4%29%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >----this as the original equation is in a different form given.  We just do not have log of a negative number,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   Base two to no power will give negative number. </SPAN>\n" );
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