Question 1027618
Starting from
{{{3^(4sqrt(x)) - 4*3^(2sqrt(x)) + 3 = 0 }}}
we will make a quick substitution...
Let {{{y = 3^(2sqrt(x))}}}
Once we do that, our original equation becomes
{{{y^2 - 4y + 3 = 0}}}
Now factor and get
(y - 3)(y - 1) = 0
so that
y = 3  and  y = 1
Now back-substitute and get
{{{3^(2sqrt(x)) = 3}}}
{{{3^(2sqrt(x)) = 1}}}
Take logs of everything and get
{{{2sqrt(x)*ln(3) = ln(3)}}}
which leads to
{{{2sqrt(x) = 1}}} and
{{{sqrt(x) = 1/2}}} so that
x = 1/4
And
{{{2sqrt(x)*ln(3) = ln(1)}}}
{{{2sqrt(x)*ln(3) = 0}}} so that
x = 0