document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=886289>Question 886289</A>: <I><SPAN STYLE=\"word-break: break-all;\"> log_3(x^(log_3(x))=4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #535878 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=535878\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> best i can do with this is as follows:\r<BR>\n" );
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document.write( "log3(x^(log3(x)) = 4\r<BR>\n" );
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document.write( "since log(a^b) = b*log(a), this equation becomes equivalent to:<BR>\n" );
document.write( "log3(x) * log3(x) = 4<BR>\n" );
document.write( "this is equivalent to:<BR>\n" );
document.write( "(log3(x))^2 = 4<BR>\n" );
document.write( "take the square root of both sides and you get:<BR>\n" );
document.write( "log3(x) = 2\r<BR>\n" );
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document.write( "this is true if and only if 3^2 = x which makes x = 9\r<BR>\n" );
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document.write( "assuming x = 9, your original equation becomes:<BR>\n" );
document.write( "log3(9^(log3(9)) = 4\r<BR>\n" );
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document.write( "log3(9) = y if and only if 3^y = 9<BR>\n" );
document.write( "this makes y = 2<BR>\n" );
document.write( "this makes log3(9) equal to 2\r<BR>\n" );
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document.write( "equation of log3(9^(log3(9)) = 4 becomes:<BR>\n" );
document.write( "log3(9^2) = 4 which becomes:<BR>\n" );
document.write( "log3(81) = 4\r<BR>\n" );
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document.write( "log3(81) = y if and only if 3^y = 81.<BR>\n" );
document.write( "thi makes y = 4 since 3^4 = 81\r<BR>\n" );
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document.write( "your equation of log3(81) = 4 becomes 4 = 4.<BR>\n" );
document.write( "this confirms the solution of x = 9 is correct.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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