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

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Solve the equation $$ \log_{3}(\log_{3}(x))=3 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\log_{3}{\left(\log_{3}{\left(xight)}ight)}=3$$
- step1: Find the domain:
  $$\log_{3}{\left(\log_{3}{\left(xight)}ight)}=3,x>1$$
- step2: Convert the logarithm into exponential form:
  $$\log_{3}{\left(xight)}=3^{3}$$
- step3: Evaluate the power:
  $$\log_{3}{\left(xight)}=27$$
- step4: Convert the logarithm into exponential form:
  $$x=3^{27}$$
- step5: Check if the solution is in the defined range:
  $$x=3^{27},x>1$$
- step6: Find the intersection:
  $$x=3^{27}$$
The solution to the equation $$ \left(\log _{3}\left(\log _{3} xight)ight)=3 $$ is $$ x = 3^{27} $$ or approximately $$ 7.625597 	imes 10^{12} $$.
$$ x = 3^{27} $$ or approximately $$ 7.625597 	imes 10^{12} $$.

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

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