SOLUTION: 3^(4√x) - 4*3^(2√x) + 3 =0 Solve for x

Algebra ->  Exponents -> SOLUTION: 3^(4√x) - 4*3^(2√x) + 3 =0 Solve for x      Log On


   

Question 1027618: 3^(4√x) - 4*3^(2√x) + 3 =0
Solve for x
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Starting from
3%5E%284sqrt%28x%29%29+-+4%2A3%5E%282sqrt%28x%29%29+%2B+3+=+0+
we will make a quick substitution...
Let y+=+3%5E%282sqrt%28x%29%29
Once we do that, our original equation becomes
y%5E2+-+4y+%2B+3+=+0
Now factor and get
(y - 3)(y - 1) = 0
so that
y = 3 and y = 1
Now back-substitute and get
3%5E%282sqrt%28x%29%29+=+3
3%5E%282sqrt%28x%29%29+=+1
Take logs of everything and get
2sqrt%28x%29%2Aln%283%29+=+ln%283%29
which leads to
2sqrt%28x%29+=+1 and
sqrt%28x%29+=+1%2F2 so that
x = 1/4
And
2sqrt%28x%29%2Aln%283%29+=+ln%281%29
2sqrt%28x%29%2Aln%283%29+=+0 so that
x = 0