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The problem shown asks to solve the equation \( 3 \left( 3^{3x - 9} \right) = 63 \).

Let's solve it step by step.

### Step 1: Simplify the equation
We start with:
\[
3 \left( 3^{3x - 9} \right) = 63
\]

Divide both sides by 3 to isolate \( 3^{3x - 9} \):
\[
3^{3x - 9} = 21
\]

### Step 2: Take the logarithm
To solve for \( x \), take the logarithm (base 3) of both sides:
\[
\log_3 \left( 3^{3x - 9} \right) = \log_3 (21)
\]

By the logarithmic property \( \log_b (b^x) = x \), we simplify the left-hand side:
\[
3x - 9 = \log_3 (21)
\]

### Step 3: Solve for \( x \)
Now solve for \( x \):
\[
3x = \log_3 (21) + 9
\]
\[
x = \frac{\log_3 (21) + 9}{3}
\]

This gives the exact solution in terms of logarithms. Depending on the options provided, the answer might match one of the following:
- \( \log_3 (21) + 9 \)

Thus, the correct answer choice is likely **\( \log_3 (21) + 9 \)**.

Would you like more details or have any questions?

Here are five follow-up questions to explore further:
1. How can logarithmic properties be used to simplify expressions?
2. What are the rules for solving exponential equations?
3. How would you solve the equation if it had a different base, like \( 5^{3x-9} = 63 \)?
4. What is the numerical value of \( \log_3(21) \)?
5. How does changing the base of the logarithm affect the solution process?

**Tip:** When dealing with exponential equations, using logarithms is a powerful tool to bring the exponent down and solve for the variable.

What is the solution to the equation 3(3^(3x-9)) = 63?

Learn how to solve the exponential equation 3(3^(3x-9)) = 63 by using logarithmic properties. Follow a detailed step-by-step solution involving division, applying logarithms, and simplifying expressions. Suitable for students in Grades 8-10.

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