https://file.aiquickdraw.com/mathbot/file/1728874855017r77815hu.jpg

The equation given in the image is:

\[
64^{5x - 1} = 16^{3x + 3}
\]

We need to find the value of \( x \) that satisfies this equation.

### Step-by-Step Solution:

1. **Expressing both sides with the same base**:
   Notice that both 64 and 16 can be written as powers of 2:
   \[
   64 = 2^6 \quad \text{and} \quad 16 = 2^4
   \]
   Therefore, we can rewrite the equation as:
   \[
   (2^6)^{5x - 1} = (2^4)^{3x + 3}
   \]

2. **Simplifying the exponents**:
   Using the property \( (a^m)^n = a^{m \cdot n} \), we can simplify both sides:
   \[
   2^{6(5x - 1)} = 2^{4(3x + 3)}
   \]
   Simplify the exponents:
   \[
   2^{30x - 6} = 2^{12x + 12}
   \]

3. **Equating the exponents**:
   Since the bases are the same, we can set the exponents equal to each other:
   \[
   30x - 6 = 12x + 12
   \]

4. **Solving for \( x \)**:
   Subtract \( 12x \) from both sides:
   \[
   18x - 6 = 12
   \]
   Add 6 to both sides:
   \[
   18x = 18
   \]
   Finally, divide both sides by 18:
   \[
   x = 1
   \]

Thus, the value of \( x \) is **1**.

---

Would you like more details or have any questions about this solution?

Here are 5 related questions to expand your understanding:
1. How would you solve the equation if the bases were not powers of the same number?
2. What other properties of exponents are useful in solving exponential equations?
3. Can you think of another example where you solve equations with powers involving different bases?
4. How can logarithms help solve exponential equations?
5. What happens if the equation contains fractional exponents?

**Tip**: Always try to rewrite exponential equations in terms of the same base, as it simplifies the comparison of exponents!

Nilai x yang memenuhi 64^{5x - 1} = 16^{3x + 3} adalah ....

Learn how to solve the exponential equation 64^(5x - 1) = 16^(3x + 3) by expressing both sides with the same base. This step-by-step solution demonstrates the use of exponent properties to find the value of x, suitable for high school math students.

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