If f(x) = x log x and g(x) = `10^(x)` , then g(f(2)) =

Options

A. 24
B. 17
C. 4
D. 2

Explanation

To solve the problem, we need to evaluate \( g(f(2)) \) where \( f(x) = x \log x \) and \( g(x) = 10^x \).

### Step 1: Calculate \( f(2) \)
We start with the function \( f(x) \):
\[ f(x) = x \log x \]
Substituting \( x = 2 \):
\[ f(2) = 2 \log 2 \]

### Step 2: Simplify \( f(2) \)
Using the property of logarithms, we can express \( 2 \log 2 \) as:
\[ f(2) = \log(2^2) = \log 4 \]

### Step 3: Calculate \( g(f(2)) \)
Now we need to evaluate \( g(f(2)) \):
\[ g(f(2)) = g(\log 4) \]
Using the definition of \( g(x) \):
\[ g(x) = 10^x \]
Substituting \( \log 4 \) into \( g \):
\[ g(\log 4) = 10^{\log 4} \]

### Step 4: Simplify \( g(\log 4) \)
Using the property of logarithms that states \( a^{\log_a b} = b \), we have:
\[ 10^{\log 4} = 4 \]

### Final Answer
Thus, the value of \( g(f(2)) \) is:
\[ \boxed{4} \]