document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=185729>Question 185729</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618250204/algebrahomeworkh>Alegbra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Explain why the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%283%2C+-1%29 ALIGN=MIDDLE  ALT=\"log+%283%2C+-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%281%2C+1%29 ALIGN=MIDDLE  ALT=\"log+%281%2C+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are not defined. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #139377 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=139377\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%283%2C+%28-1%29%29 ALIGN=MIDDLE  ALT=\"log+%283%2C+%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=log+%283%2C+%28-1%29%29 ALIGN=MIDDLE  ALT=\"y=log+%283%2C+%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set \"y\" equal to the expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5Ey=-1 ALIGN=MIDDLE  ALT=\"3%5Ey=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the property <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y=\log_{b}\left(x\right) \Leftrightarrow b^y=x\"> to rewrite the equation.\r<BR>\n" );
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document.write( "Now the question is: what value of \"y\" will make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5Ey ALIGN=MIDDLE  ALT=\"3%5Ey\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to -1? Since there is NO value of \"y\" that will make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5Ey ALIGN=MIDDLE  ALT=\"3%5Ey\"   DISABLED_style= \"max-width:90%; height:auto;\" > negative (because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5Ey ALIGN=MIDDLE  ALT=\"3%5Ey\"   DISABLED_style= \"max-width:90%; height:auto;\" > is ALWAYS positive), this means that there are no solutions to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5Ey=-1 ALIGN=MIDDLE  ALT=\"3%5Ey=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This in turn means that you CANNOT take the log of a negative number (or zero). \r<BR>\n" );
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document.write( "So that's why <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%283%2C+%28-1%29%29 ALIGN=MIDDLE  ALT=\"log+%283%2C+%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is undefined\r<BR>\n" );
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document.write( "In fact, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%28b%2C+%28x%29%29 ALIGN=MIDDLE  ALT=\"log+%28b%2C+%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is undefined where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%3E1 ALIGN=MIDDLE  ALT=\"b%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=0 ALIGN=MIDDLE  ALT=\"x%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%281%2C+%281%29%29 ALIGN=MIDDLE  ALT=\"log+%281%2C+%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%2810%2C+%281%29%29%2Flog+%2810%2C+%281%29%29 ALIGN=MIDDLE  ALT=\"log+%2810%2C+%281%29%29%2Flog+%2810%2C+%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the change of base formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%29%29=log%2810%2C%28x%29%29%2Flog%2810%2C%28b%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%29%29=log%2810%2C%28x%29%29%2Flog%2810%2C%28b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to rewrite the expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F0 ALIGN=MIDDLE  ALT=\"0%2F0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the log of 1 to get 0.\r<BR>\n" );
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document.write( "Now remember, division by zero is undefined. So we cannot go further.\r<BR>\n" );
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document.write( "So this shows us that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%281%2C+%281%29%29 ALIGN=MIDDLE  ALT=\"log+%281%2C+%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is undefined. </SPAN>\n" );
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