document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=936231>Question 936231</A>: <I><SPAN STYLE=\"word-break: break-all;\"> log base 9 of 6=a, log base 27 of 18=b. Express b in terms of a. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569872 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=569872\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log(9,6) = a<BR>\n" );
document.write( "log(27,18) = b<BR>\n" );
document.write( "you want to express b in terms of a.\r<BR>\n" );
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document.write( "log(9,6) = a if and only if 9^a = 6<BR>\n" );
document.write( "log(27,18) = b if and only if 27^b = 18\r<BR>\n" );
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document.write( "since 9 = 3^2, then 9^a can be expressed as (3^2)^a which becomes 3^(2a) and you get:\r<BR>\n" );
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document.write( "9^a = 6 becomes 3^(2a) = 6\r<BR>\n" );
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document.write( "since 27 = 3^3, then 27^b can be expressed as (3^3)^b which becomes 3^(3b) and you get:\r<BR>\n" );
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document.write( "27^b = 18 becomes 3^(3b) = 18\r<BR>\n" );
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document.write( "if you divide both sides of this equation by 3, you will get:\r<BR>\n" );
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document.write( "3^(3b) / 3 = 6\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "3^(3b-1) = 6\r<BR>\n" );
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document.write( "you now have:\r<BR>\n" );
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document.write( "3^(2a) = 6 and 3^(3b-1) = 6\r<BR>\n" );
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document.write( "this can only be true if 2a = 3b-1\r<BR>\n" );
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document.write( "solve for b and you get b = (2a+1) / 3\r<BR>\n" );
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document.write( " </SPAN>\n" );
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