document.write( "Question 1043767: Solve the simultaneous equations giving your answer in logarithmic form:
\n" ); document.write( "3^(X-y) = 9^y
\n" ); document.write( "2^X = 6(2^y) \n" ); document.write( "

Algebra.Com's Answer #658964 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve the simultaneous equations giving your answer in logarithmic form:
\n" ); document.write( " $\"3%5E%28X-y%29+=+9%5Ey\"$
\n" ); document.write( " $\"2%5EX+=+6%282%5Ey%29\"$
\n" ); document.write( ":
\n" ); document.write( "we can greatly simplify the 1st equation; 9 = 3^2, therefore we can write it
\n" ); document.write( " $\"3%5E%28X-y%29+=+3%5E%282y%29\"$
\n" ); document.write( "therefore
\n" ); document.write( "x - y = 2y
\n" ); document.write( "x = 3y
\n" ); document.write( "the 2nd equation
\n" ); document.write( " $\"2%5EX+=+6%282%5Ey%29\"$
\n" ); document.write( " $\"2%5Ex%2F2%5Ey\"$ = 6
\n" ); document.write( "Replace x with 3y
\n" ); document.write( " $\"2%283y%29%2F2%5Ey\"$ = 6
\n" ); document.write( "therefore
\n" ); document.write( " $\"2%5E%282y%29\"$ = 6
\n" ); document.write( "2y*log(2) = log(6)
\n" ); document.write( "2y = $\"log%286%29%2Flog%282%29\"$
\n" ); document.write( "2y = 2.525
\n" ); document.write( "y = 2.525/2
\n" ); document.write( "y = 1.2925
\n" ); document.write( "Find x
\n" ); document.write( "x = 3(1.2925)
\n" ); document.write( "x = 3.877
\n" ); document.write( "But they want it in logarithmic form
\n" ); document.write( "log(x) = .5885
\n" ); document.write( "log(y) = .1114 \n" ); document.write( "

\n" );