document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090405>Question 1090405</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve for x. log X base5= log5 base X +2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704846 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=704846\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>The equation is<br><BR>\n" );
document.write( "log_5(x) = log_x(5)+2<br><BR>\n" );
document.write( "Use the fact that log_a(b) and log_b(a) are reciprocals to rewrite log_x(5) as 1/log_5(x):<br><BR>\n" );
document.write( "log_5(x) = 1/log_5(x) + 2<br><BR>\n" );
document.write( "Then multiply both sides by log_5(x) to yield a quadratic equation with log_5(x) as the \"variable\":<br><BR>\n" );
document.write( "(log_5(x))^2 = 1 + 2log_5(x)<br><BR>\n" );
document.write( "(log_5(x))^2 - 2log_5(x) - 1 = 0<br><BR>\n" );
document.write( "Then use the quadratic formula to find the two values of log_5(x), and from those value find the two values of x. </SPAN>\n" );
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