https://file.aiquickdraw.com/mathbot/file/17269978173701fkw3rfo.jpg

Let's solve the two problems shown in the image:

### 3. Jika \( 4^x + 4^x = 34 \), tentukan nilai \( 2^x + 2^x \)!

We are given the equation:
\[
4^x + 4^x = 34
\]
First, simplify the left-hand side:
\[
2 \cdot 4^x = 34
\]
Now divide both sides by 2:
\[
4^x = 17
\]
We know that \( 4^x = (2^2)^x = (2^x)^2 \), so substitute:
\[
(2^x)^2 = 17
\]
Now, take the square root of both sides:
\[
2^x = \sqrt{17}
\]

Finally, calculate the value of \( 2^x + 2^x \):
\[
2^x + 2^x = 2 \cdot 2^x = 2 \cdot \sqrt{17}
\]
Thus, the value of \( 2^x + 2^x \) is:
\[
2 \sqrt{17}
\]

### 4. Tentukan nilai dari:
\[
\frac{4^{130} \cdot 4^{128} - 60}{4^{128} - 4}
\]
First, simplify the numerator:
\[
4^{130} \cdot 4^{128} = 4^{130 + 128} = 4^{258}
\]
Thus, the numerator becomes:
\[
4^{258} - 60
\]
Now the entire expression is:
\[
\frac{4^{258} - 60}{4^{128} - 4}
\]

To simplify further, we would need to factor or reduce the expression, but without further factorization possibilities, we can leave it in this form for now. It would depend on numerical evaluation or further algebraic manipulation.

---

Would you like more details on any of the steps, or have any specific questions? Here are five questions to expand your understanding:

1. How do we handle exponential expressions with different bases in equations?
2. What are the rules for simplifying exponential terms with the same base?
3. How can we further manipulate the expression in problem 4?
4. What methods exist for solving quadratic or higher-degree exponential equations?
5. How can the properties of logarithms help in simplifying exponential expressions?

**Tip:** When solving exponential equations, expressing everything in terms of the same base is often the key to simplification!

3. Jika 4^x + 4^x = 34, tentukan nilai 2^x + 2^x. 4. Tentukan nilai dari 4^130 . 4^128 - 60 / 4^128 - 4

Learn how to solve exponential equations like 4^x + 4^x = 34 and find the value of 2^x + 2^x. Also, discover how to simplify complex expressions involving large exponents such as 4^130 / 4^128. Suitable for advanced high school students in Grades 10-12.

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