https://file.aiquickdraw.com/mathbot/file/1727163876593do0soryj.jpg

The equation presented in the image is:

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

We will solve for \( x \) by expressing both sides of the equation in terms of powers of 2. Let's break it down:

1. Express 64 and 16 as powers of 2:
   \[
   64 = 2^6 \quad \text{and} \quad 16 = 2^4
   \]

2. Substitute these into the equation:
   \[
   (2^6)^{5x - 1} = (2^4)^{3x + 3}
   \]

3. Apply the power of a power rule \((a^m)^n = a^{m \cdot n}\):
   \[
   2^{6(5x - 1)} = 2^{4(3x + 3)}
   \]

4. Simplify both exponents:
   \[
   2^{30x - 6} = 2^{12x + 12}
   \]

5. Since the bases are the same, equate the exponents:
   \[
   30x - 6 = 12x + 12
   \]

6. Solve for \( x \):
   \[
   30x - 12x = 12 + 6
   \]
   \[
   18x = 18
   \]
   \[
   x = 1
   \]

Thus, the value of \( x \) is \( \boxed{1} \).

Would you like any further details or clarifications?

Here are 5 related questions to expand your understanding:
1. How can you solve similar equations with different bases?
2. What if the bases were not powers of the same number? How would the approach change?
3. How can you check the solution by plugging it back into the original equation?
4. What is the significance of the power of a power rule in exponent equations?
5. How do logarithms help in solving equations where bases aren't easily comparable?

**Tip:** When solving exponential equations, always try to express both sides with the same base—it simplifies the process greatly!

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 as powers of 2. This step-by-step solution applies exponent rules and power of a power rule, suitable for high school students in Grades 9-12.

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