document.write( "Question 91693: how do i solve this system of equations
\n" ); document.write( " $\"+ln+x+=+3ln+y\"$
\n" ); document.write( " $\"+3%5Ex+=+27%5Ey+\"$ \n" ); document.write( "

Algebra.Com's Answer #66590 by psbhowmick(878) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"ln%28x%29+=+3ln%28y%29\"$
\n" ); document.write( " $\"ln%28x%29+=+ln%28y%5E3%29\"$
\n" ); document.write( " $\"ln%28x%29+-+ln%28y%5E3%29+=+0\"$
\n" ); document.write( " $\"ln%28x%2Fy%5E3%29+=+0\"$
\n" ); document.write( " $\"x%2Fy%5E3+=+1\"$
\n" ); document.write( " $\"x+=+y%5E3\"$ __________ (1)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"3%5Ex+=+27%5Ey\"$
\n" ); document.write( " $\"3%5Ex+=+%283%5E3%29%5Ey\"$
\n" ); document.write( " $\"3%5Ex+=+3%5E%283y%29\"$
\n" ); document.write( " $\"x+=+3y\"$ ___________ (2)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Substituting x from (1) in (2)
\n" ); document.write( " $\"y%5E3+=+3y\"$
\n" ); document.write( " $\"y%5E3+-+3y+=+0\"$
\n" ); document.write( " $\"y%28y%5E2+-+3%29+=+0\"$
\n" ); document.write( " $\"y%28y+%2B+sqrt%283%29%29%28y+-+sqrt%283%29%29+=+0\"$
\n" ); document.write( "Either $\"y+=+0\"$ , $\"y+=+-+sqrt%283%29\"$ or $\"y+=+sqrt%283%29\"$
\n" ); document.write( "Accordingly, $\"x+=+0\"$ , $\"x+=+-+3sqrt%283%29\"$ or $\"x+=+3sqrt%283%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "But since logarithm of negative numbers is undefined so $\"x+=+-3sqrt%283%29\"$ , $\"y+=+-sqrt%283%29\"$ is not a solution.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Hence, the solutions are $\"x+=+0\"$ , $\"+y+=+0\"$ and $\"x+=+3sqrt%283%29\"$ , $\"y+=+sqrt%283%29\"$ . \n" ); document.write( "

\n" );