$$ g ( x ) = \log _ { a } x \quad x = a ^ { 2 } $$

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To analyze the function $$ g(x) = \log_a x $$ with the condition $$ x = a^2 $$, we can substitute $$ x $$ in the logarithmic function.

1. **Substituting $$ x $$**:
   $$
   g(a^2) = \log_a (a^2)
   $$

2. **Using the properties of logarithms**:
   The logarithm of a power can be simplified using the property $$ \log_b (b^k) = k $$:
   $$
   g(a^2) = \log_a (a^2) = 2
   $$

Thus, when $$ x = a^2 $$, the value of $$ g(x) $$ is:
$$
g(a^2) = 2
$$

In summary, for $$ g(x) = \log_a x $$ with $$ x = a^2 $$, we find that $$ g(a^2) = 2 $$.
$$ g(a^2) = 2 $$

\( g ( x ) = \log _ { a } x \quad x = a ^ { 2 } \)

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