document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=29899>Question 29899</A>: <I><SPAN STYLE=\"word-break: break-all;\"> log cube root of x = square root of log x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #16700 by </B><A HREF=/tutors/aboutme.mpl?userid=kev82><B>kev82(151)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kev82><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=16700\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\log\sqrt[3]{x}=\sqrt{\log x}\">\r<BR>\n" );
document.write( "\n" );
document.write( "The LHS can be rewritten as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\frac{\log x}{3}=\sqrt{\log x}\">\r<BR>\n" );
document.write( "\n" );
document.write( "Now we can get rid of that nasty square root by squaring, but beware we might also introduce more solutions, so any answers we get at the end will have to be checked. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?(\log x)^2=9\log x\">.\r<BR>\n" );
document.write( "\n" );
document.write( "We can now factorize, and solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\log x\">\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?(\log x)(\log x - 9)=0\">. So either <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\log x=0\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\log x=9\">.\r<BR>\n" );
document.write( "\n" );
document.write( "Now I don't know what base your logorthms are in, but I'm going to assume base 10. So we have either <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?x=1\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?x=1000000000\">. If you put these back into the equation, I think you'll find they both work.\r<BR>\n" );
document.write( "\n" );
document.write( "Hope that helps,<BR>\n" );
document.write( "Kev </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );