Question 1154501
.
<pre>

The original equation is

    {{{(sqrt(x))^(log((x)))}}} = 100.


The domain is  { x | x > 0 }.


The equation is equivalent to

    {{{x^((1/2)*log((x)))}}} = 100.


Square both sides.   You will get

    {{{x^(log((x)))}}} = 10000.


Take logarithm base 10 from both sides.  You will get

    log(x) * log(x) = log(10000),   or

    (log(x))^2 = log(10000),  or

    (log(x))^2 = 4.


Take square root from both sides.  You will get

    log(x) = +/- 2.


So we have two solutions

    1)  log(x) = 2,  x = {{{10^2}}} = 100,   and


    2)  log((x) = -2,  x = {{{10^(-2)}}} = {{{1/100}}}.


<U>ANSWER</U>.  The original equation has two solutions,  x = 100  and  x = {{{1/100}}}.
</pre>

Solved.