document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167773>Question 167773</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, the following question is from a past exam paper on algebra & complex numbers that I am looking at in order to revise for my Calculus exam.  I have the answer in front of me, but I do not quite understand the working behind it, so if you could clear that up for me I would be grateful.\r<BR>\n" );
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document.write( "QUESTION SIX<BR>\n" );
document.write( "Solve the following equation for x in terms of q:  2^(3x-1)=7^(x-q)\r<BR>\n" );
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document.write( "The assessment schedule says that the answer should be: x=(ln2-qln7)/(3ln2-ln7) or equivalent </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123674 by </B><A HREF=/tutors/aboutme.mpl?userid=rviksub><B>rviksub(2)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rviksub><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=123674\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2^(3x-1)=7^(x-q) \r<BR>\n" );
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document.write( "Use the property ln a^b=b ln a\r<BR>\n" );
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document.write( "Take ln on both sides,<BR>\n" );
document.write( "ln 2^(3x-1)=ln 7^(x-q) <BR>\n" );
document.write( "(3x-1)ln2=(x-q)ln7<BR>\n" );
document.write( "3xln2-ln2=xln7-qln7<BR>\n" );
document.write( "3x ln2-x ln7=ln2 -q ln7<BR>\n" );
document.write( "» x(3ln2-ln7)=ln2-qln7<BR>\n" );
document.write( "» x= (ln2-qln7)/(3ln2-ln7)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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