If `f(x)=e^(x)` and `g(x)=logx`, then gof is____________.

Answer

To find \( g(f(x)) \) where \( f(x) = e^x \) and \( g(x) = \log x \), we will follow these steps:

### Step 1: Identify the functions
We have:
- \( f(x) = e^x \)
- \( g(x) = \log x \)

### Step 2: Substitute \( f(x) \) into \( g(x) \)
We need to find \( g(f(x)) \). This means we will substitute \( f(x) \) into \( g(x) \):
\[ g(f(x)) = g(e^x) \]

### Step 3: Apply the function \( g \)
Now, we apply the function \( g \) to \( e^x \):
\[ g(e^x) = \log(e^x) \]

### Step 4: Simplify \( \log(e^x) \)
Using the logarithmic identity \( \log(a^b) = b \cdot \log(a) \), we can simplify:
\[ \log(e^x) = x \cdot \log(e) \]
Since \( \log(e) = 1 \) (the logarithm of a number to its own base is 1), we have:
\[ \log(e^x) = x \cdot 1 = x \]

### Final Answer
Thus, \( g(f(x)) = x \).

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