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If f(x)=log(e)[log(e)x]. then what is f ...

If `f(x)=log_(e)[log_(e)x]`. then what is f (e) equal to ?

A

`e^(-1)`

B

e

C

1

D

0

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The correct Answer is:
To solve the problem, we need to evaluate the function \( f(x) = \log_e(\log_e x) \) at \( x = e \). ### Step-by-Step Solution: 1. **Write down the function**: \[ f(x) = \log_e(\log_e x) \] 2. **Substitute \( x = e \)**: \[ f(e) = \log_e(\log_e e) \] 3. **Evaluate \( \log_e e \)**: - We know that \( \log_e e = 1 \) because the logarithm of a number to its own base is always 1. \[ f(e) = \log_e(1) \] 4. **Evaluate \( \log_e(1) \)**: - The logarithm of 1 to any base is 0. \[ f(e) = 0 \] 5. **Final answer**: \[ f(e) = 0 \] ### Summary: Thus, the value of \( f(e) \) is 0.
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