We are given the logarithmic equation:

\[
\log_3(8 - 5x) = 2
\]

To solve for \(x\), follow these steps:

1. **Convert the logarithmic equation to its exponential form**:
   \[
   8 - 5x = 3^2
   \]
   Since the base of the logarithm is 3, we raise 3 to the power on the right side of the equation.

2. **Simplify the exponential**:
   \[
   8 - 5x = 9
   \]

3. **Solve for \(x\)**:
   - Subtract 8 from both sides:
     \[
     -5x = 9 - 8
     \]
     \[
     -5x = 1
     \]

   - Divide both sides by -5:
     \[
     x = \frac{1}{-5} = -\frac{1}{5}
     \]

Thus, the solution is:

\[
x = -\frac{1}{5}
\]

---

Would you like more details on logarithmic conversions or have any questions? Here are some related questions you might find helpful:

1. What are the properties of logarithms, and how are they applied in different problems?
2. How can you solve logarithmic equations involving multiple logarithmic terms?
3. What are the common bases of logarithms, and how do they affect equation solving?
4. Can logarithmic equations have no solution or more than one solution?
5. How are logarithmic and exponential functions related?

**Tip:** Always remember that logarithms can only be applied to positive numbers!

Learn how to solve the logarithmic equation log_3(8 - 5x) = 2 with a clear step-by-step breakdown. This solution involves converting the logarithmic equation to its exponential form and solving for x. Ideal for students in Grades 9-10.

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