`e^(ln ln 7)=7`
(a) True (b) False

Answer

To determine whether the statement \( e^{(\ln \ln 7)} = 7 \) is true or false, we can follow these steps:

### Step 1: Understand the expression
We need to evaluate the left-hand side of the equation \( e^{(\ln \ln 7)} \).

### Step 2: Apply the property of logarithms
Using the property of logarithms that states \( e^{\ln x} = x \), we can rewrite our expression:
\[ e^{(\ln \ln 7)} = \ln 7 \]

### Step 3: Compare \( \ln 7 \) with 7
Now we need to compare \( \ln 7 \) with 7. We know that:
- \( \ln 7 \) is the natural logarithm of 7, which is a value less than 7 since the natural logarithm of any number greater than 1 is always less than the number itself.

### Step 4: Conclusion
Since \( \ln 7 \) is not equal to 7, we conclude that:
\[ e^{(\ln \ln 7)} \neq 7 \]
Thus, the statement \( e^{(\ln \ln 7)} = 7 \) is **False**.

### Final Answer
(b) False

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