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The given equation is:

\[
3^{x+3} = \frac{1}{81}
\]

### Step-by-step solution:

1. **Rewrite \( \frac{1}{81} \) as a power of 3**:
   \[
   81 = 3^4 \quad \text{so} \quad \frac{1}{81} = 3^{-4}
   \]

   Therefore, the equation becomes:
   \[
   3^{x+3} = 3^{-4}
   \]

2. **Set the exponents equal to each other**:
   Since the bases are the same (both are 3), we can equate the exponents:
   \[
   x + 3 = -4
   \]

3. **Solve for \( x \)**:
   \[
   x = -4 - 3 = -7
   \]

Thus, the value of \( x \) is \(-7\), but none of the provided multiple-choice answers match this result. There might be a mistake in the problem or options provided.

Would you like more details or have any questions?

### Relative questions:
1. What happens if the base is different?
2. How can we handle negative exponents in similar equations?
3. What if \( 81 \) was written as \( 9^2 \)? How would that change the solution?
4. How can logarithms be used to solve more complex exponential equations?
5. How do exponents affect the shape of graphs for exponential functions?

**Tip:** Always try to rewrite constants as powers of the same base when solving exponential equations. This simplifies the comparison of exponents.

Nilai x dari persamaan eksponen berikut: 3^(x+3) = 1/81 adalah...

Learn how to solve the exponential equation 3^(x+3) = 1/81. This step-by-step solution explains how to rewrite 1/81 as a power of 3 and equate the exponents. Suitable for students in Grades 9-10.

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