https://file.aiquickdraw.com/mathbot/file/1726104454632mbgyw25e.jpg

The equation shown in the image is:

\[
\log_3(25 - x^2) = 2
\]

### Step-by-step Solution:

1. **Rewrite the logarithmic equation in exponential form:**

   Using the property of logarithms:  
   \[
   \log_b(y) = x \quad \text{implies} \quad b^x = y
   \]
   In our case, this becomes:
   \[
   3^2 = 25 - x^2
   \]
   Simplifying:
   \[
   9 = 25 - x^2
   \]

2. **Isolate \(x^2\):**

   \[
   25 - 9 = x^2
   \]
   \[
   16 = x^2
   \]

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

   \[
   x = \pm \sqrt{16}
   \]
   \[
   x = \pm 4
   \]

### Final Answer:
The solutions are \( x = 4 \) and \( x = -4 \).

Would you like more details, or do you have any questions?

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Here are 5 related questions to explore:
1. How do you solve logarithmic equations with different bases?
2. What are the properties of logarithms, and how do they help in solving equations?
3. How can you check if both solutions \( x = 4 \) and \( x = -4 \) are valid in the context of logarithms?
4. What happens if the base of the logarithm is less than 1?
5. How do you solve logarithmic inequalities?

**Tip:** Always check the domain of the logarithmic function when solving equations! Make sure the argument inside the logarithm is positive.

This page explains how to solve the logarithmic equation log_3(25 - x^2) = 2 using the properties of logarithms and quadratic equations. Step-by-step instructions are provided to rewrite the equation in exponential form and solve for x. Suitable for students in Grades 9-12.

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