document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=957849>Question 957849</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the properties of logarithms to solve the given equation. <BR>\n" );
document.write( "log2(log2 x) = 2<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #585352 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=585352\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log2(log2(x)) = 2 if and only if 2^2 = log2(x).\r<BR>\n" );
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document.write( "2^2 = 4, so this becomes if and only if 4 = log2(x).\r<BR>\n" );
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document.write( "log2(x) = 4 if and only if 2^4 = x which means that x = 16.\r<BR>\n" );
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document.write( "solution is that x = 16.\r<BR>\n" );
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document.write( "equation becomes:\r<BR>\n" );
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document.write( "log2(log2(16)) = 2\r<BR>\n" );
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document.write( "you can confirm this is true by using the log conversion formula of log2(x) = log(x) / log(2)\r<BR>\n" );
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document.write( "log2(log2(16)) = 2 becomes log2(log(16)/log(2)) = 2\r<BR>\n" );
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document.write( "log(16)/log(2) = 4, so the equation becomes log2(4) = 2\r<BR>\n" );
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document.write( "log2(4) = 2 becomes log(4) / log(2) = 2 which becomes 2 = 2.\r<BR>\n" );
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document.write( "this confirms the solution is correct.\r<BR>\n" );
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