Question

If \( x>0 \) and \( \log x + \log \left( \log x \right) + \log \left( \log \log x \right) + \dots = 4 \), then \[ x \text{ equals} \]

• A. 9
• B. 81
• C. 27
• D. 1

Hint:

When dealing with logarithmic equations, simplify step by step using logarithmic identities.

Answer 1

The Correct Option is C

Step 1: Understanding the equation.
The equation involves logarithms and can be solved by successively applying logarithmic properties to simplify the terms. After simplification, we find that \( x = 27 \).

Step 2: Conclusion.
Thus, the correct answer is option (C).

Final Answer: \[ \boxed{\text{(C) } 27} \]