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Let's solve the equation step-by-step:

The equation is:

\[
3^{5x - 3} = 9^{2x}
\]

### Step 1: Express \(9^{2x}\) as a power of 3.
We know that \(9 = 3^2\), so we can rewrite the equation:

\[
3^{5x - 3} = (3^2)^{2x}
\]

### Step 2: Simplify the exponents.
Using the exponent rule \((a^m)^n = a^{m \cdot n}\), we simplify the right-hand side:

\[
3^{5x - 3} = 3^{4x}
\]

### Step 3: Set the exponents equal to each other.
Since the bases are the same, we can set the exponents equal:

\[
5x - 3 = 4x
\]

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

Subtract \(4x\) from both sides:

\[
5x - 4x - 3 = 0
\]

This simplifies to:

\[
x - 3 = 0
\]

So:

\[
x = 3
\]

### Final Answer:
The correct solution is \( \boxed{x = 3} \), which corresponds to option **b**.

Would you like any further explanation on this? Here are some additional questions you can explore:

1. How can you generalize solving equations with different bases?
2. What other methods can you use to solve exponential equations?
3. What happens if the equation had been \(9^{2x+1}\)? 
4. How can logarithms be applied to solve similar exponential equations?
5. What are the properties of exponents that allow for simplifying expressions like \(9^{2x}\)?

**Tip**: Always try to express both sides of an equation with the same base when solving exponential equations.

Solve for x in the following equation: 3^(5x - 3) = 9^(2x)

Learn how to solve the exponential equation 3^(5x - 3) = 9^(2x) with a step-by-step guide. This problem uses the exponent rule and properties of exponents to simplify and solve the equation. Suitable for high school students in Grades 9-11.

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