document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=243826>Question 243826</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how many real solutions does the following equation have?\r<BR>\n" );
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document.write( "log(4x-15)=logx+log(x+4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #178598 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=178598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log(4x-15) = log(x) + log(x+4)\r<BR>\n" );
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document.write( "becomes:\r<BR>\n" );
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document.write( "log(4x-15) = log(x*(x+4)) because log(a*b) = log(a) + log(b)\r<BR>\n" );
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document.write( "In this case, a was equal to x and b was equal to (x+4)\r<BR>\n" );
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document.write( "if log(4x-15) = log(x*(x+4)) then:\r<BR>\n" );
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document.write( "4x-15 = x*(x+4) which becomes:\r<BR>\n" );
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document.write( "4x-15 = x^2 + 4x\r<BR>\n" );
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document.write( "subtract 4x from both sides of this equation to get:\r<BR>\n" );
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document.write( "x^2 + 4x - 4x = -15 which becomes:\r<BR>\n" );
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document.write( "x^2 = -15\r<BR>\n" );
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document.write( "take the square root of both sides of this equation to get:\r<BR>\n" );
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document.write( "x = +/- sqrt(-15)\r<BR>\n" );
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document.write( "since you are taking the square root of a negative number, and the result of that is not real, then the number of real solutions that this equation has is 0.<BR>\n" );
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