https://file.aiquickdraw.com/mathbot/file/1727063428280ab8c9hjc.jpg

The equation given in the image is:

\[
2^{3x + 2} = 256
\]

### Step-by-step solution:

1. **Express 256 as a power of 2:**

   We know that:
   \[
   256 = 2^8
   \]
   So, the equation becomes:
   \[
   2^{3x + 2} = 2^8
   \]

2. **Since the bases are the same, equate the exponents:**

   \[
   3x + 2 = 8
   \]

3. **Solve for \(x\):**
   \[
   3x = 8 - 2
   \]
   \[
   3x = 6
   \]
   \[
   x = \frac{6}{3} = 2
   \]

### Final Answer:
The value of \( x \) is \( 2 \).

---

Would you like any additional details or explanations on this solution?

Here are 5 related questions you might find helpful:

1. What are the steps to solve equations where bases are not the same?
2. How can you verify if \(x = 2\) is correct?
3. What other values could 256 take in different base forms?
4. How do we solve exponential equations when the exponents contain more complex terms?
5. Can this problem be solved graphically, and if so, how?

**Tip:** Always check whether both sides of the equation can be expressed as powers of the same base to simplify exponential equations easily!

Tentukan nilai x yang memenuhi persamaan (2)^{3x+2} = 256

Learn how to solve the exponential equation (2)^{3x+2} = 256 with a step-by-step explanation. This algebraic problem involves the concepts of exponentiation and equating powers. Suitable for students in Grades 9-10.

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