document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=606063>Question 606063</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I know this shouldn't be hard, we are doing a study sheet for a test and can't get past the second problem.\r<BR>\n" );
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document.write( "simplify each logarithm (a calculator should not be needed)\r<BR>\n" );
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document.write( "log base (1/3) 9  so this is 1/3^x equals 9<BR>\n" );
document.write( "if I use the change of base formula I  get -.5  or 1/2 but when I try to work 1/3^(1/2)  I don't get 9<BR>\n" );
document.write( "what am I doing wrong, and I can't use a calculator anyway so how do I do this without the change of base formula?\r<BR>\n" );
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document.write( "thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #381897 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=381897\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" src=\"http://latex.codecogs.com/gif.latex?\LARGE x = \log_{\frac{1}{3}}\left(9\right)\" title=\"x\" />\r<BR>\n" );
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document.write( "Convert this equation to exponential form to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%5Ex=9 ALIGN=MIDDLE  ALT=\"%281%2F3%29%5Ex=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now let's solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%5Ex=9 ALIGN=MIDDLE  ALT=\"%281%2F3%29%5Ex=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%5E%28-1%29%29%5Ex=3%5E2 ALIGN=MIDDLE  ALT=\"%283%5E%28-1%29%29%5Ex=3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%28-1%2Ax%29=3%5E2 ALIGN=MIDDLE  ALT=\"3%5E%28-1%2Ax%29=3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%28-x%29=3%5E2 ALIGN=MIDDLE  ALT=\"3%5E%28-x%29=3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the bases are equal (to 3), the exponents must be equal. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x=2 ALIGN=MIDDLE  ALT=\"-x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we let <IMG STYLE=\"max-width:80%;\" src=\"http://latex.codecogs.com/gif.latex?\LARGE x = \log_{\frac{1}{3}}\left(9\right)\" title=\"x\" /> at the top of the problem, we can say that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://latex.codecogs.com/gif.latex?\LARGE \text{\color{red}Answer:} \ \color{blue}\boxed{\log_{\frac{1}{3}}\left(9\right) = \color{red} -2}\" title=\"x\" />\r<BR>\n" );
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document.write( "Note: you can use the change of base formula to get the same answer of -2.\r<BR>\n" );
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