Thank you for the clarification. Let's solve the problem correctly with the base 3:

### Problem:
\[
\log_3 (\log_2 x) = 1
\]

### Step 1: Convert the logarithmic equation to an exponential equation
The equation \(\log_3 (\log_2 x) = 1\) can be rewritten using the definition of logarithms:

\[
\log_2 x = 3^1
\]

### Step 2: Simplify the equation
Since \(3^1 = 3\), we have:

\[
\log_2 x = 3
\]

### Step 3: Solve for \(x\)
To solve for \(x\), rewrite the logarithmic equation in its exponential form:

\[
x = 2^3
\]

### Step 4: Calculate the value of \(x\)
Now, calculate \(2^3\):

\[
2^3 = 8
\]

### Final Answer
Thus, the correct solution to the equation is:

\[
\boxed{8}
\]

Would you like further details or have any additional questions?

Here are 5 related questions to consider:
1. How do you identify the base of a logarithm and use it in solving equations?
2. What is the importance of converting logarithmic equations into exponential form?
3. How would the solution change if the original equation was \(\log_3 (\log_2 x) = 2\) instead?
4. What steps would you follow if the equation involved a logarithm with a base greater than 10?
5. How does the logarithm base affect the solution of the equation?

**Tip:** When working with logarithms, carefully check the base to ensure the correct conversion to an exponential form. This helps in avoiding mistakes during calculations.

Learn how to solve the logarithmic equation log base 3 of log base 2 of x equals 1 with a detailed step-by-step solution. This problem involves logarithmic and exponential equations, suitable for high school level students.

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