The problem asks for the steps to solve the equation $\frac{5}{2}(3)^x - 1 = 9$. We need to identify the correct order of operations to isolate $x$.

1. Problem Description

The problem asks for the steps to solve the equation $\frac{5}{2}(3)^x - 1 = 9$. We need to identify the correct order of operations to isolate $x$.

2. Solution Steps

First, we want to isolate the term with the exponent. We add 1 to both sides of the equation:

$\frac{5}{2}(3)^x - 1 + 1 = 9 + 1$

$\frac{5}{2}(3)^x = 10$

Next, we multiply both sides by $\frac{2}{5}$ to isolate the exponential term:

$\frac{2}{5} \cdot \frac{5}{2}(3)^x = \frac{2}{5} \cdot 10$

$(3)^x = 4$

Finally, to solve for $x$, we take the logarithm base 3 of both sides:

$log_3(3^x) = log_3(4)$

$x = log_3(4)$

Therefore, the steps are:

Step 1: Add 1 to both sides.

Step 2: Multiply both sides by 2/

5. Step 3: Take the logarithm base 3 of both sides.

3. Final Answer

Step 1: Add 1 to both sides.

Step 2: Multiply both sides by 2/

5. Step 3: Take the logarithm base 3 of both sides.