A function `f(x)=log(g(x))`, where `g(x)` is any function of x.
If `g(x)=e^(x)`. Then `f(f(x))` is equal to :

Options

A. a. e
B. b. `e^(x)`
C. c. `logx`
D. d. none of these

Answer

To solve the problem, we need to find \( f(f(x)) \) where \( f(x) = \log(g(x)) \) and \( g(x) = e^x \).

### Step-by-Step Solution:

1. **Identify the function \( g(x) \)**:
We are given that \( g(x) = e^x \).

2. **Find \( f(x) \)**:
We can substitute \( g(x) \) into the function \( f(x) \):
\[ f(x) = \log(g(x)) = \log(e^x) \]

3. **Simplify \( f(x) \)**:
Using the property of logarithms, \( \log(e^x) = x \):
\[ f(x) = x \]

4. **Find \( f(f(x)) \)**:
Now we need to find \( f(f(x)) \):
\[ f(f(x)) = f(x) \]
Since we have already established that \( f(x) = x \), we can substitute:
\[ f(f(x)) = f(x) = x \]

5. **Conclusion**:
Therefore, \( f(f(x)) = x \).

### Final Answer:
\[ f(f(x)) = x \]