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The solutions to the equation \(\log(x^{\log{x}}) = 4\) are:

\[
x = e^2 \quad \text{or} \quad x = e^{-2}
\]

Would you like further details or clarification?

Here are 5 related questions to explore:
1. What is the process to solve logarithmic equations involving powers of logs?
2. How is the base \(e\) (natural logarithm) used in equations like this?
3. What are the properties of the logarithmic function that helped solve this?
4. How would this equation change if the log base was 10 instead of \(e\)?
5. What is the significance of both positive and negative solutions?

**Tip:** When solving logarithmic equations, always check if the solutions are valid, as logarithms require positive arguments.

Solve the equation log(x^(log(x))) = 4 for x.

This page provides a detailed solution to the logarithmic equation log(x^(log(x))) = 4. The solution involves using properties of logarithms and exponential functions to find that x equals either e^2 or e^(-2). Suitable for students in advanced high school or undergraduate mathematics.

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