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.