https://file.aiquickdraw.com/mathbot/file/1728387126101o6mxrfg3.jpg

The equation in the image is:

\[
\log_x(\log_2 256) = 3
\]

### Step 1: Simplify \(\log_2 256\)
We know that \(256 = 2^8\), so:

\[
\log_2 256 = 8
\]

Now, substitute this back into the original equation:

\[
\log_x 8 = 3
\]

### Step 2: Solve for \(x\)
The equation \(\log_x 8 = 3\) can be rewritten in exponential form:

\[
x^3 = 8
\]

Now, solve for \(x\):

\[
x = \sqrt[3]{8} = 2
\]

Thus, the value of \(x\) is:

\[
x = 2
\]

Would you like more details on any step, or do you have further questions?

Here are 5 related questions:
1. What is the general process to change a logarithmic equation into exponential form?
2. How does the base of the logarithm affect the calculation in a logarithmic equation?
3. How do you solve for \(x\) when the logarithmic equation involves higher powers?
4. What other numbers have integer logarithmic values in different bases?
5. How can you apply the change of base formula in logarithmic equations?

**Tip:** Always remember that converting between logarithmic and exponential forms is a powerful technique for solving equations involving logarithms.

Solve for the value of x in the equation log_x(log_2 256) = 3.

Learn how to solve the logarithmic equation log_x(log_2 256) = 3 with a step-by-step explanation. This solution involves simplifying logarithms and converting to exponential form. Suitable for high school students.

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