document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211487>Question 211487</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do i solve...<BR>\n" );
document.write( "logx (cubed root of 9) = 1/6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #159895 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=159895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> problem is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%2Croot%283%2C9%29%29+=+1%2F6 ALIGN=MIDDLE  ALT=\"log%28x%2Croot%283%2C9%29%29+=+1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "by the definition of logarithms, this equation is true if and only if:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%281%2F6%29+=+root%283%2C9%29 ALIGN=MIDDLE  ALT=\"x%5E%281%2F6%29+=+root%283%2C9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "that equation is the same as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%281%2F6%29+=+9%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"x%5E%281%2F6%29+=+9%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "take the 6th power of both sides of this equation to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E%281%2F6%29%29%5E6+=+%289%5E%281%2F3%29%29%5E6 ALIGN=MIDDLE  ALT=\"%28x%5E%281%2F6%29%29%5E6+=+%289%5E%281%2F3%29%29%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "by the laws of exponents, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5Ea%29%5Eb+=+x%5E%28a%2Ab%29 ALIGN=MIDDLE  ALT=\"%28x%5Ea%29%5Eb+=+x%5E%28a%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > so the equation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E%281%2F6%29%29%5E6+=+%289%5E%281%2F3%29%29%5E6 ALIGN=MIDDLE  ALT=\"%28x%5E%281%2F6%29%29%5E6+=+%289%5E%281%2F3%29%29%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+9%5E2 ALIGN=MIDDLE  ALT=\"x+=+9%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this makes x = 81<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let's see if this holds water.<BR>\n" );
document.write( "the original equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%2Croot%283%2C9%29%29+=+1%2F6 ALIGN=MIDDLE  ALT=\"log%28x%2Croot%283%2C9%29%29+=+1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we replace x with 81 to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2881%2Croot%283%2C9%29%29+=+1%2F6 ALIGN=MIDDLE  ALT=\"log%2881%2Croot%283%2C9%29%29+=+1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this is true if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%5E%281%2F6%29+=+root%283%2C9%29 ALIGN=MIDDLE  ALT=\"81%5E%281%2F6%29+=+root%283%2C9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "using the calculator, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%5E%281%2F6%29 ALIGN=MIDDLE  ALT=\"81%5E%281%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2.080083823...<BR>\n" );
document.write( "using the calculator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C9%29 ALIGN=MIDDLE  ALT=\"root%283%2C9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = cube root of 9 = 2.080083823...<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "looks like they're equivalent.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer is x = 81<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you can also solve this using your calculator by converting from the log to the base of 81, to the log to the base 10 which your calculator can handle.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2881%2Croot%283%2C9%29%29+=+1%2F6 ALIGN=MIDDLE  ALT=\"log%2881%2Croot%283%2C9%29%29+=+1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "using the logarithm base conversion formula,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2881%2Croot%283%2C9%29%29+=+%28log%2810%2Croot%283%2C9%29%29%29%2F%28log%2810%2C81%29%29 ALIGN=MIDDLE  ALT=\"log%2881%2Croot%283%2C9%29%29+=+%28log%2810%2Croot%283%2C9%29%29%29%2F%28log%2810%2C81%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "using the calculator,<BR>\n" );
document.write( "(log(10,root(3,9)))/(log(10,81))}}} becomes:<BR>\n" );
document.write( ".318080836/1.908485019 = .16666666...<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "This is equivalent to 1/6 confirming that the answer is correct.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer is:<BR>\n" );
document.write( "x = 81<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );