To solve the equation \(-6\log_3(x - 3) = -24\), follow these steps:

1. **Divide both sides by -6** to isolate the logarithm:
   \[
   \log_3(x - 3) = 4
   \]

2. **Rewrite the logarithmic equation in its exponential form**:
   \[
   x - 3 = 3^4
   \]

3. **Calculate \(3^4\)**:
   \[
   3^4 = 81
   \]
   So, \(x - 3 = 81\).

4. **Add 3 to both sides** to solve for \(x\):
   \[
   x = 81 + 3 = 84
   \]

So, the solution is \(x = 84\).

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. What is the general method for solving logarithmic equations?
2. How do you convert a logarithmic equation into its exponential form?
3. What are the properties of logarithms that can be used to simplify logarithmic expressions?
4. Can logarithmic equations have more than one solution? Why or why not?
5. How would the solution change if the logarithm had a different base?

**Tip:** When solving logarithmic equations, always ensure the argument of the logarithm is positive, as logarithms are undefined for non-positive arguments.

Learn how to solve the logarithmic equation -6log3(x-3)=-24 with a step-by-step solution. This problem involves logarithms and exponential equations, covering key properties and formulas. Suitable for students in Grades 10-12.

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