document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254894>Question 254894</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let logX(base A) = C , and logX(baseB) = D. Find the general statement that expresses logX(base AB), in terms of C and D.\r<BR>\n" );
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document.write( "Please help anyone. I think the answer is C+D or C+D/2. All help is much appreciated.\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187233 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=187233\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use several change of bases:<BR>\n" );
document.write( "(i) log_A(x) = C<BR>\n" );
document.write( "By change of base rules, we get<BR>\n" );
document.write( "(ii) log(x)/log(A) = C<BR>\n" );
document.write( "and solving for log(A) we get<BR>\n" );
document.write( "(iii) log(A) = log(x)/C<BR>\n" );
document.write( "--<BR>\n" );
document.write( "(iv) log_B(x) = D<BR>\n" );
document.write( "By change of base rules, we get<BR>\n" );
document.write( "(v) log(x)/log(B) = D<BR>\n" );
document.write( "and solving for log(B) we get<BR>\n" );
document.write( "(vi) log(B) = log(x)/D<BR>\n" );
document.write( "--<BR>\n" );
document.write( "Now,<BR>\n" );
document.write( "(vii) log_AB(x) <BR>\n" );
document.write( "becomes<BR>\n" );
document.write( "(viii) log(x)/log(AB) <BR>\n" );
document.write( "which is expanded to<BR>\n" );
document.write( "(ix) log(x) / (log(A) + log(B)).<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "by substitution of (iii) and (vi) into (ix), we get<BR>\n" );
document.write( "(x) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%29+%2F+%28log%28x%29%2FC+%2B+log%28x%29%2FD%29 ALIGN=MIDDLE  ALT=\"log%28x%29+%2F+%28log%28x%29%2FC+%2B+log%28x%29%2FD%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "by adding the denominator fractions, we get<BR>\n" );
document.write( "(xi)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%29+%2F+%28%28Dlog%28x%29+%2B+Clog%28x%29%29%2FCD%29 ALIGN=MIDDLE  ALT=\"log%28x%29+%2F+%28%28Dlog%28x%29+%2B+Clog%28x%29%29%2FCD%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "factoring out the log(x) gives us<BR>\n" );
document.write( "(xii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%29+%2F+%28log%28x%29%28C+%2B+D%29%29div%28CD%29 ALIGN=MIDDLE  ALT=\"log%28x%29+%2F+%28log%28x%29%28C+%2B+D%29%29div%28CD%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and finally the answer as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD%2F%28C%2BD%29%29 ALIGN=MIDDLE  ALT=\"CD%2F%28C%2BD%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );