To find the value of \( a \) where the logarithmic function \( g(x) = \log_{25}(x) \) contains the point \( (a, 3) \), we start by interpreting this point. The point \( (a, 3) \) means that:
\[ g(a) = 3 \]
This can be translated into the logarithmic equation:
\[ \log_{25}(a) = 3 \]
Using the properties of logarithms, we can rewrite this in exponential form:
\[ a = 25^3 \]
Now, we calculate \( 25^3 \):
\[ 25 = 5^2 \implies 25^3 = (5^2)^3 = 5^{2 \times 3} = 5^6 \]
Now, let's compute \( 5^6 \):
\[ 5^6 = 15625 \]
Thus, the value of \( a \) is
\[ \boxed{15625} \]