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The image contains a mathematical problem. Let's analyze and solve it step-by-step.

**Given Equation:**

\[ 3 \log_5 (3x - 2) = 9 \]

**Step 1: Simplify the equation**

First, we can divide both sides of the equation by 3:

\[ \log_5 (3x - 2) = 3 \]

**Step 2: Exponentiate both sides**

To remove the logarithm, we exponentiate both sides of the equation with base 5:

\[ 3x - 2 = 5^3 \]

Since \( 5^3 = 125 \):

\[ 3x - 2 = 125 \]

**Step 3: Solve for \( x \)**

Add 2 to both sides:

\[ 3x = 127 \]

Then, divide by 3:

\[ x = \frac{127}{3} \]

So, the solution to the equation is:

\[ x = \frac{127}{3} \approx 42.33 \]

Would you like more details or have any questions? Here are some further questions you might consider:

1. How do you convert logarithmic equations to exponential form?
2. What are the properties of logarithms that can simplify solving equations?
3. How do you solve logarithmic equations with different bases?
4. Can you solve an equation involving natural logarithms (\(\ln\))?
5. How does the change of base formula work for logarithms?

**Tip:** When solving logarithmic equations, remember to check that the argument of the logarithm is positive, as logarithms are only defined for positive real numbers.

Learn how to solve the logarithmic equation 3*log_5(3x - 2) = 9 step-by-step with a detailed explanation. This problem involves logarithm properties and solving exponential equations. Suitable for students in Grades 10-12.

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