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The problem asks for the solution to the equation:

\[
\log_2(9x) - \log_2 3 = 3
\]

Let's solve this step by step:

### Step 1: Apply the logarithmic property
Using the property of logarithms:

\[
\log_b A - \log_b B = \log_b \left(\frac{A}{B}\right)
\]

This simplifies the equation as follows:

\[
\log_2 \left(\frac{9x}{3}\right) = 3
\]

### Step 2: Simplify the fraction
Simplify the expression inside the logarithm:

\[
\frac{9x}{3} = 3x
\]

Now the equation becomes:

\[
\log_2(3x) = 3
\]

### Step 3: Eliminate the logarithm
To eliminate the logarithm, we rewrite the equation in exponential form:

\[
3x = 2^3
\]

Simplifying \(2^3 = 8\), we get:

\[
3x = 8
\]

### Step 4: Solve for \(x\)

\[
x = \frac{8}{3}
\]

Thus, the solution is:

\[
x = \frac{8}{3}
\]

The correct answer is \( \boxed{x = \frac{8}{3}} \).

Would you like more details on any of these steps? Here are five related questions to consider:

1. How do logarithmic properties help in simplifying equations?
2. What is the process of converting a logarithmic equation to an exponential one?
3. Why is it important to apply the correct logarithmic rules in equations like this?
4. How can we verify the solution by substituting \(x = \frac{8}{3}\) back into the original equation?
5. What are some common mistakes to avoid when dealing with logarithmic equations?

**Tip:** Always remember that logarithmic subtraction can be transformed into a division inside a single logarithm.

What is the solution to \log_2(9x) - \log_2 3 = 3?

Learn how to solve the logarithmic equation \log_2(9x) - \log_2 3 = 3. This problem explores key logarithmic concepts, applying properties of logarithms to simplify and solve the equation step by step. Suitable for students in Grades 9-12.

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