If `f(x)=log_(10)x and g(x)=e^(ln x) and h(x)=f [g(x)]`, then find the value of h(10).

Answer

To solve the problem step by step, we will follow the definitions of the functions given and calculate \( h(10) \).

### Step 1: Define the functions
We have the following functions defined:
- \( f(x) = \log_{10} x \)
- \( g(x) = e^{\ln x} \)
- \( h(x) = f[g(x)] \)

### Step 2: Simplify \( g(x) \)
We know from properties of logarithms and exponentials that:
\[ g(x) = e^{\ln x} = x \]
This is because the exponential function \( e \) and the natural logarithm \( \ln \) are inverse functions.

### Step 3: Substitute \( g(x) \) into \( h(x) \)
Now we substitute \( g(x) \) into \( h(x) \):
\[ h(x) = f[g(x)] = f[x] \]
This means that \( h(x) \) is simply \( f(x) \).

### Step 4: Calculate \( h(10) \)
Now we need to find \( h(10) \):
\[ h(10) = f(10) \]
Substituting into the function \( f \):
\[ f(10) = \log_{10}(10) \]

### Step 5: Evaluate \( \log_{10}(10) \)
We know that:
\[ \log_{10}(10) = 1 \]

### Final Answer
Thus, the value of \( h(10) \) is:
\[ h(10) = 1 \]