document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=890826>Question 890826</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hey can you solve this please?: log4/9[(2x+1)/(x+3)]=-1/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #539309 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=539309\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if i understand this correctly, the problem is:\r<BR>\n" );
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document.write( "log4/9(2x+1)/(x+3)=-1/2\r<BR>\n" );
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document.write( "this is true if and only if (4/9)^(-1/2) = (2x+1)/(x+3)\r<BR>\n" );
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document.write( "(4/9)^(-1/2) = 1/(4/9)^(1/2) = 1/(2/3) = 3/2\r<BR>\n" );
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document.write( "equation becomes:\r<BR>\n" );
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document.write( "3/2 = (2x+1)/(x+3)\r<BR>\n" );
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document.write( "multiply both sides of the equation by 2 and multiply both sides of the equation by (x+3) to get:\r<BR>\n" );
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document.write( "3(x+3) = 2(2x+1)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "3x+9 = 4x+2\r<BR>\n" );
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document.write( "subtract 3x from both sides of the equation and subtract 2 from both sides of the equation to get:\r<BR>\n" );
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document.write( "7 = x\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "x = 7\r<BR>\n" );
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document.write( "when x = 7, your equation of log4/9[(2x+1)/(x+3)]=-1/2 becomes:\r<BR>\n" );
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document.write( "log4/9((2*7+1)/(7+3)) = -1/2 which becomes:\r<BR>\n" );
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document.write( "log4/9((15/10)) = -1/2 which becomes:\r<BR>\n" );
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document.write( "log4/9((3/2) = -1/2\r<BR>\n" );
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document.write( "you can solve this by translating it into an exponential equation.\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "log4/9((3/2) = -1/2 if and only if (4/9)^(-1/2) = 3/2\r<BR>\n" );
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document.write( "(4/9)^(-1/2) is equal to 1 / (4/9)^(1/2.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "1/(4/9)^(1/2) = 3/2 which becomes:\r<BR>\n" );
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document.write( "1/(2/3) = 3/2 which becomes:\r<BR>\n" );
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document.write( "3/2 = 3/2, confirming that x = 7 is the solution.\r<BR>\n" );
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document.write( "you could also have solved it by using the log base conversion formula and then using your calculator to get the log.\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "log4/9((3/2) = -1/2\r<BR>\n" );
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document.write( "log conversion formula says that log4/9(3/2) = LOG(3/2)/LOG(4/9)\r<BR>\n" );
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document.write( "LOG is equal to log10 which is the same as log to the base of 10 which is what your calculator can handle.\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "LOG(3/2)/LOG(4/9) = -1/2\r<BR>\n" );
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document.write( "use your calculator to get:\r<BR>\n" );
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document.write( "LOG(3/2)/LOG(4/9) = -.5.\r<BR>\n" );
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document.write( "-.5 is the same as -1/2 so you're good and the solution is x = 7.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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