For what value of x is the equation below valid?

Questions
,
1

\left[ \left( (i!)^{\cos(x!) + \sin(i!)} \right)! \right]^i = \phi^{\phi!}

2

You can try this:

f[x_] = (((I!)^(Cos[x!] + Sin[I!]))!)^I - GoldenRatio^GoldenRatio!
sol = Solve[f[x] == 0, x]
f[x] /. sol // N

However, a complex number elevated to a complex number is a problematic concept:

ComplexPlot3D[Evaluate[N[f[x]]], {x, -10 - 10 I, 10 + 10 I}, 
 PlotRange -> {-.1, 1.5}]