document.write( "Question 1027618: 3^(4√x) - 4*3^(2√x) + 3 =0\r
\n" ); document.write( "\n" ); document.write( "Solve for x \n" ); document.write( "

Algebra.Com's Answer #642861 by fractalier(6550) $\"\"$ $\"About$

You can put this solution on YOUR website!
Starting from
\n" ); document.write( " $\"3%5E%284sqrt%28x%29%29+-+4%2A3%5E%282sqrt%28x%29%29+%2B+3+=+0+\"$
\n" ); document.write( "we will make a quick substitution...
\n" ); document.write( "Let $\"y+=+3%5E%282sqrt%28x%29%29\"$
\n" ); document.write( "Once we do that, our original equation becomes
\n" ); document.write( " $\"y%5E2+-+4y+%2B+3+=+0\"$
\n" ); document.write( "Now factor and get
\n" ); document.write( "(y - 3)(y - 1) = 0
\n" ); document.write( "so that
\n" ); document.write( "y = 3 and y = 1
\n" ); document.write( "Now back-substitute and get
\n" ); document.write( " $\"3%5E%282sqrt%28x%29%29+=+3\"$
\n" ); document.write( " $\"3%5E%282sqrt%28x%29%29+=+1\"$
\n" ); document.write( "Take logs of everything and get
\n" ); document.write( " $\"2sqrt%28x%29%2Aln%283%29+=+ln%283%29\"$
\n" ); document.write( "which leads to
\n" ); document.write( " $\"2sqrt%28x%29+=+1\"$ and
\n" ); document.write( " $\"sqrt%28x%29+=+1%2F2\"$ so that
\n" ); document.write( "x = 1/4
\n" ); document.write( "And
\n" ); document.write( " $\"2sqrt%28x%29%2Aln%283%29+=+ln%281%29\"$
\n" ); document.write( " $\"2sqrt%28x%29%2Aln%283%29+=+0\"$ so that
\n" ); document.write( "x = 0 \n" ); document.write( "

\n" );