https://file.aiquickdraw.com/mathbot/file/17305182401608591icyv.jpg

The equation in the image is:

\[
3^x = 9
\]

To solve for \( x \), let's express both sides in terms of the same base, if possible.

### Solution:
1. Notice that 9 can be written as a power of 3: 
   \[
   9 = 3^2
   \]

2. Substitute \( 9 \) with \( 3^2 \):
   \[
   3^x = 3^2
   \]

3. Since the bases are the same, we can set the exponents equal to each other:
   \[
   x = 2
   \]

### Answer:
\[
x = 2
\]

Would you like more details on exponential equations or have any specific questions?

Here are five related questions to explore further:
1. How do you solve exponential equations when the bases are different?
2. What happens if the exponent is a fraction?
3. Can you solve \( 2^x = 16 \) using a similar approach?
4. What are some real-world applications of exponential equations?
5. How do logarithms help in solving exponential equations?

**Tip:** When solving exponential equations, try to express both sides with the same base to simplify the solution process.

Learn how to solve the exponential equation 3^x = 9 by expressing both sides with the same base. This problem covers key algebraic concepts and exponential properties, suitable for students in Grades 8-10.

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