document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1057131>Question 1057131</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I just need someone to explain this and why 2 is the answer:<BR>\n" );
document.write( "3^(log base 9 (4))= 2\r<BR>\n" );
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document.write( "I'm not sure how to write out log base correctly, but it's log(4) with the base of 9. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #672208 by </B><A HREF=/tutors/aboutme.mpl?userid=solve_for_x><B>solve_for_x(190)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solve_for_x><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=672208\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When you have something like log (base 9) 4, you can rewrite it as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+4+%2F+log+9 ALIGN=MIDDLE  ALT=\"log+4+%2F+log+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And when you do that, you can use any base for the logarithms that you want.\r<BR>\n" );
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document.write( "So, instead of using the common base-10 log, we can write is using a base-3 log:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log9+%284%29+=+log+4+%2F+log+9+=+log3+%284%29+%2F+log3+%289%29 ALIGN=MIDDLE  ALT=\"log9+%284%29+=+log+4+%2F+log+9+=+log3+%284%29+%2F+log3+%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But log3 (9) = 2:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log9+%284%29+=+log3+%284%29+%2F+2 ALIGN=MIDDLE  ALT=\"log9+%284%29+=+log3+%284%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log3%284%29%2F2 ALIGN=MIDDLE  ALT=\"log3%284%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in place of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log9%284%29 ALIGN=MIDDLE  ALT=\"log9%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%28log3%284%29%2F2%29 ALIGN=MIDDLE  ALT=\"3%5E%28log3%284%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which equals:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%5E%28log3%284%29%29%29++ ALIGN=MIDDLE  ALT=\"sqrt%283%5E%28log3%284%29%29%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%28log3%284%29%29+=+4+ ALIGN=MIDDLE  ALT=\"3%5E%28log3%284%29%29+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the expression is equal to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29+=+2 ALIGN=MIDDLE  ALT=\"sqrt%284%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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