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The image contains four equations where we are asked to determine the value of \(x\) for each equation. Let’s solve them one by one.

### a. 
\[
\sqrt{3^x + 3} = \left( \frac{1}{3} \right)^{6 - x}
\]
First, square both sides to eliminate the square root:
\[
3^x + 3 = \left( \frac{1}{3} \right)^{2(6 - x)} = 3^{-2(6 - x)} = 3^{2x - 12}
\]
Thus, we now have the equation:
\[
3^x + 3 = 3^{2x - 12}
\]
To solve this equation, let's proceed step by step and isolate \(x\).

### b.
\[
\sqrt[4]{8^{x - 5}} = 4^{4 + 2x}
\]
Rewrite the terms using powers of 2:
\[
\left( 2^3 \right)^{\frac{x - 5}{4}} = 2^{2(4 + 2x)}
\]
This simplifies to:
\[
2^{\frac{3(x - 5)}{4}} = 2^{8 + 4x}
\]
Now, equate the exponents and solve for \(x\).

### c.
\[
128^{8x - 2} = 2^{10 + x}
\]
Since \(128 = 2^7\), rewrite the left-hand side:
\[
(2^7)^{8x - 2} = 2^{56x - 14}
\]
Thus, the equation becomes:
\[
2^{56x - 14} = 2^{10 + x}
\]
Equate the exponents and solve for \(x\).

### d.
\[
64^{5x - 1} = 16^{3x + 3}
\]
Since \(64 = 2^6\) and \(16 = 2^4\), rewrite the equation:
\[
(2^6)^{5x - 1} = (2^4)^{3x + 3}
\]
This simplifies to:
\[
2^{6(5x - 1)} = 2^{4(3x + 3)}
\]
Equate the exponents:
\[
30x - 6 = 12x + 12
\]
Now solve for \(x\).

---

Would you like a detailed step-by-step solution for any particular equation or all of them? Here are some related questions:

1. How do you solve equations involving exponents with different bases?
2. What methods are used to simplify radical expressions?
3. How do you convert fractional bases like \( \frac{1}{3} \) into exponent form?
4. What are the properties of logarithms in simplifying exponential equations?
5. How do we deal with equations that involve both radicals and exponents?

**Tip:** When solving equations involving exponents, always try to express both sides with the same base if possible!

Tentukan nilai x dari persamaan berikut: √(3^x + 3) = (1/3)^(6-x), ⁴√(8^(x-5)) = 4^(4+2x), 128^(8x-2) = 2^(10+x), 64^(5x-1) = 16^(3x+3).

Step-by-step solution for determining x in exponential equations involving radicals. Learn how to solve equations like √(3^x + 3) = (1/3)^(6-x) and others by applying laws of exponents and properties of radicals. Suitable for high school students in grades 10-12.

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