document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=966004>Question 966004</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2log5(x)= -log2(25)<BR>\n" );
document.write( "Solve for x.<BR>\n" );
document.write( "the 5 next to log is small and the 2 next to log is small </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #590425 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=590425\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> assuming you can use a calculator, then the easiest way to solve this is to convert everything to base 10 that the calculator can handle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "or you can convert everything to base e that the calculator can also handle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "base 10 is LOG function of calculator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "base e is LN function of calculator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your equation is 2L5(x) = -L2(25)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "L5 means log to the base 5.<BR>\n" );
document.write( "L2 means log to the base 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "L5(x) = LOG(x)/LOG(5)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "L2(25) = LOG(25)/LOG(2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your problem becomes 2LOG(x)/LOG(5) = -LOG(25)/LOG(2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for LOG(x) to get LOG(x) = LOG(5) * -LOG(25) / LOG(2) / 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "use your calculator to solve for LOG(x) to get LOG(x) = -1.622958091\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is true if and only if 10^-1.622958091 = x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x to get x = .0238254937\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's your answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace x in your original equation and you will see that the equation is true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your original equation, after it has been converted to base 10, is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2LOG(x)/LOG(5) = -LOG(25)/LOG(2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace x with .0238254937 and the eqution becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2LOG(.0238254937)/LOG(5) = -LOG(25)/LOG(2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve this equation using your calculator and you will get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-4.64385619 = -4.64385619, which is true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the solution looks good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );