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 evaluate the functions \( f(x) \), \( g(x) \), and \( h(x) \) as defined in the question.

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

### Step 2: Simplify \( g(x) \)
Using the property of logarithms and exponentials, we know that:
\[ g(x) = e^{\ln x} = x \]
Thus, \( g(x) \) simplifies to \( x \).

### Step 3: Define \( h(x) \)
Now, we can express \( h(x) \):
\[ h(x) = f(g(x)) = f(x) \]
Since \( g(x) = x \), we have:
\[ h(x) = f(x) = \log_{10} x \]

### Step 4: Find \( h(10) \)
Now we need to find \( h(10) \):
\[ h(10) = f(10) = \log_{10} 10 \]

### Step 5: Evaluate \( \log_{10} 10 \)
Using the property of logarithms, we know:
\[ \log_{10} 10 = 1 \]

### Conclusion
Thus, the value of \( h(10) \) is:
\[ \boxed{1} \]