document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=573761>Question 573761</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please answer my question.\r<BR>\n" );
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document.write( "Kindly solve the equation and find the solution set.\r<BR>\n" );
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document.write( "log base of 3 (2x-3)+log base of 3 (x-4)=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #368867 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=368867\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log base of 3 (2x-3)+log base of 3 (x-4)=1<BR>\n" );
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document.write( "Since log a + log b = log(ab), we can combine the sum into a single logarithm:<BR>\n" );
document.write( "log3((2x-3)(x-4)) = 1<BR>\n" );
document.write( "Now get rid of the logarithm:<BR>\n" );
document.write( "3^(log3((2x-3)(x-4)) = 3^1<BR>\n" );
document.write( "(2x-3)(x-4) = 3<BR>\n" );
document.write( "Multiply using FOIL and collect terms:<BR>\n" );
document.write( "2x^2 - 11x + 9 = 0<BR>\n" );
document.write( "Factor:<BR>\n" );
document.write( "(2x-9)(x-1) = 0<BR>\n" );
document.write( "This gives x=1, x=9/2<BR>\n" );
document.write( "The 1st solution is disallowed, since this would result in the logarithm of a negative number<BR>\n" );
document.write( "So the answer is x=9/2<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "log3((9-3)(9/2-8/2)) = log3(6*1/2) = log3(3) = 1 </SPAN>\n" );
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