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Let's go through the three questions one by one.

### Question 1: 
**What does ln 1 = (Natural log of 1)?**
- The natural logarithm of 1 is **0** because \(\ln(1) = 0\). The logarithm function asks, "To what power should we raise \(e\) to get 1?" Since \(e^0 = 1\), the answer is **0**.

### Question 2:
**Solve for the unknown: \(\ln(e^7) = x\)**

Using logarithmic properties:
\[
\ln(e^7) = 7 \cdot \ln(e) = 7 \cdot 1 = 7
\]
So, \(x = 7\).

### Question 3:
**Solve for the unknown: \(\log_4 8 = \log_4 x\)**

Since the logs have the same base, we can equate the arguments:
\[
8 = x
\]
Thus, \(x = 8\).

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Would you like further details or clarification on any of these solutions? Here are 5 related questions to explore further:

1. What is the natural logarithm of a number close to 0, like \(\ln(0.1)\)?
2. What happens when you apply the natural logarithm to negative numbers?
3. Can the base of a logarithm in a given problem be a fractional number like 1/2?
4. How do you solve logarithmic equations with different bases?
5. What is the derivative of a logarithmic function like \(\ln(x)\)?

**Tip**: Remember, logarithmic functions can simplify exponentials, and they are handy for solving equations involving powers!

What does ln 1 equal? Solve ln(e^7) = x. Solve log_4(8) = log_4(x).

Explore solutions to logarithmic and exponential problems, including natural logarithms like ln(1), solving ln(e^7), and equating log_4(8) with log_4(x). Detailed explanations of key concepts such as logarithmic identities and properties of exponents.

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