document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103958>Question 103958</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve:  log base 5 (7+x) + log base 5 (8-x) - log base 5 2 = 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75687 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=75687\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log base 5 (7+x) + log base 5 (8-x) - log base 5 2 = 2<BR>\n" );
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document.write( "Keep the base 5 in mind.<BR>\n" );
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document.write( "log[(7+x)(8-x)/2] = 2\r<BR>\n" );
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document.write( "log[56+x-x^2] = 2<BR>\n" );
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document.write( "Now, using the fact that the base is 5 you get:\r<BR>\n" );
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document.write( "56+x-x^2 = 5^2<BR>\n" );
document.write( "x^2-x-31=0<BR>\n" );
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document.write( "x = [1 +- sqrt(1-4*-31]/2\r<BR>\n" );
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document.write( "x = [1 +- sqrt(125)]/2\r<BR>\n" );
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document.write( "x = [1 +- 5sqrt(5)]/2\r<BR>\n" );
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document.write( "x = [1 + 5sqrt(5)]/2 = 6.09...<BR>\n" );
document.write( "OR<BR>\n" );
document.write( "x = [1 - 5sqrt(5)]/2 = -5.09...<BR>\n" );
document.write( "Check these answers in the original equation<BR>\n" );
document.write( "to see if either is extraneous.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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