document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=34700>Question 34700</A>: <I><SPAN STYLE=\"word-break: break-all;\"> \"SOLVING EXPONENTIAL AND LOGARITHMIC EQUATIONS\" ---> why is it that when any value of X results in a log of a negative number, it must be rejected??? \r<BR>\n" );
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document.write( "it's from a workbook that my professor created - not a textbook. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #20957 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=20957\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider an example log (-10) = x<BR>\n" );
document.write( "The exponential meaning of this is <BR>\n" );
document.write( "10^x=-10<BR>\n" );
document.write( "But no power of 10 can produce a negative number.<BR>\n" );
document.write( "Oh?<BR>\n" );
document.write( "What if we make the base -10 ?<BR>\n" );
document.write( "Then (-10)^1 = -10<BR>\n" );
document.write( "so, -10 works for this case; but what about (-10)^(1/2).<BR>\n" );
document.write( "That is imaginary.  <BR>\n" );
document.write( "Negative bases just don't give the properties that log<BR>\n" );
document.write( "functions need.<BR>\n" );
document.write( "So the base must be positive and its powers can never be negative.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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