document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=303588>Question 303588</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve this equation:\r<BR>\n" );
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document.write( "(log base6 x)^2 - 3*(log base 6 x) - 2 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #217584 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=217584\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (log base6 x)^2 - 3*(log base 6 x) - 2 = 0<BR>\n" );
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document.write( "Let log6(x) = w<BR>\n" );
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document.write( "Substitute to get:<BR>\n" );
document.write( "w^2 - 3w -2 = 0<BR>\n" );
document.write( "Solve for \"w\":<BR>\n" );
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document.write( "w = [3 +- sqrt(9 -4*-2)]/2<BR>\n" );
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document.write( "w = [3 +- sqrt(17)]/2<BR>\n" );
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document.write( "w = (3+sqrt(17))/2 or w = (3-sqrt(17))/2<BR>\n" );
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document.write( "Substitute to solve for \"x\":<BR>\n" );
document.write( "log6(x) = {3+sqrt(17)]/2 or log6(x) = (3-sqrt(17))/2<BR>\n" );
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document.write( "x = 6^(3.5616) or x = 6^(-0.5616)<BR>\n" );
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document.write( "x = 2.7351 or x = 0.3656<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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