\log_{2}\left(\log_{2}\left(x\right)\right)=4

We are given the equation:

\[
\log_{2}\left(\log_{2}(x)\right) = 4
\]

### Step 1: Solve the outer logarithmic equation
First, solve the equation \(\log_{2}(y) = 4\) where \(y = \log_{2}(x)\). This is done by rewriting the logarithmic equation in its exponential form:

\[
y = 2^4 = 16
\]

Thus, \(\log_{2}(x) = 16\).

### Step 2: Solve the inner logarithmic equation
Now that we have \(\log_{2}(x) = 16\), rewrite this in exponential form:

\[
x = 2^{16} = 65536
\]

### Final Answer:
The solution is:

\[
x = 65536
\]

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How do you solve logarithmic equations with different bases?
2. What are the properties of logarithms?
3. How does the change of base formula work for logarithms?
4. How do you graph a logarithmic function like \(\log_{2}(x)\)?
5. What are the inverse functions of logarithmic functions?

**Tip:** When solving logarithmic equations, always remember to rewrite the logarithm as an exponent to simplify!

Learn how to solve the logarithmic equation log2(log2(x)) = 4 using a step-by-step approach. This solution involves converting logarithms to their exponential form. Ideal for students in Grades 9-12 studying logarithms and exponential functions.

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