Solve for $$ x $$ : $$ \left(\log _{2}\left(\log _{2} x\right)\right)=3 $$ $$ x=\square $$

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Solve the equation $$ \log_{2}(\log_{2}(x))=3 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\log_{2}{\left(\log_{2}{\left(x\right)}\right)}=3$$
- step1: Find the domain:
  $$\log_{2}{\left(\log_{2}{\left(x\right)}\right)}=3,x>1$$
- step2: Convert the logarithm into exponential form:
  $$\log_{2}{\left(x\right)}=2^{3}$$
- step3: Evaluate the power:
  $$\log_{2}{\left(x\right)}=8$$
- step4: Convert the logarithm into exponential form:
  $$x=2^{8}$$
- step5: Evaluate the power:
  $$x=256$$
- step6: Check if the solution is in the defined range:
  $$x=256,x>1$$
- step7: Find the intersection:
  $$x=256$$
The solution to the equation $$ \left(\log _{2}\left(\log _{2} x\right)\right)=3 $$ is $$ x=256 $$.
$$ x=256 $$

Solve for \( x \) : \( \left(\log _{2}\left(\log _{2} x\right)\right)=3 \) \( x=\square \)

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