document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033620>Question 1033620</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1/3 log3 x^6 +1/6 log3 x^6 - 1/9 log3x<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 #648419 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=648419\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1/3 * log3(x^6) + 1/6 * log3(x^6) - 1/9 * log3(x) is your expression.\r<BR>\n" );
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document.write( "since 1/3 * log3(x^6) is equivalent to log3((x^6)^(1/3)) which is equal to log3(x^2), ...\r<BR>\n" );
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document.write( "and since 1/6 * log3(x^6) is equivalent to log3((x^6)^(1/6)) which is equal to log3(x), ...\r<BR>\n" );
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document.write( "and since 1/9 * log3(x) is equivalent to log3((x^(1/9)) which is equal to log3(x^(1/9)), your expression becomes ...\r<BR>\n" );
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document.write( "log3(x^2) + log3(x) - log3(x^(1/9).\r<BR>\n" );
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document.write( "since log3(x^2) + log3(x) is equivalent to log3(x^2*x) which is equal to log3(x^3), your expression becomes ...\r<BR>\n" );
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document.write( "log3(x^3) - log3(x^(1/9)).\r<BR>\n" );
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document.write( "since log3(x^3) - log3(x^(1/9)) is equivalent to log3(x^3 / x^(1/9)) which is equal to log3(x^(26/9), your expression becomes ...\r<BR>\n" );
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document.write( "log3(x^(26/9).\r<BR>\n" );
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document.write( "i believe that's as simple as it gets.\r<BR>\n" );
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document.write( "you can confirm that your solution is correct by assigning a random value to x and then evaluating the original expression and the final expression to see that they give you the same answer.\r<BR>\n" );
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document.write( "i chose x = 5 and i got the same answer for both the original expression and the final expression.<BR>\n" );
document.write( "my answer was 4.232145727.<BR>\n" );
document.write( "it helps to use the log conversion formula.<BR>\n" );
document.write( "log3(x) = log10(x) / log10(3).<BR>\n" );
document.write( "this allows you to use your calculator since the calculator log function assumes log10.<BR>\n" );
document.write( "using your calculator, you would simply enter log3(x) as log(x) / log(3).<BR>\n" );
document.write( "for the final expression, i entered log3(x^(26/9)) as log(5^(26/9)) / log(3).<BR>\n" );
document.write( "for the original expression, i entered 1/3 * log3(x^6) + 1/6 * log3(x^6) - 1/9 * log3(x) as (1/3 * log(5^6) + 1/6 * log(5^6) - 1/9 * log(5)) / log(3).\r<BR>\n" );
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