To find the value of \( a \) for the logarithmic function \( g(x) = \log_{25}(x) \) that contains the point \( (a, 3) \), we use the relationship between exponential and logarithmic functions.
Given that \( f(x) = 25^x \) contains the point \( (3, 0.064) \), we can verify this point:
\[ f(3) = 25^3 \]
Calculating \( 25^3 \):
\[ 25^3 = 25 \cdot 25 \cdot 25 = 625 \cdot 25 = 15625 \]
This means the point \( (3, 0.064) \) is incorrect, as \( 25^3 \neq 0.064 \).
Instead, let's check what \( 25^x \) would equal when \( x = 3 \):
\[ f(3) = 25^3 = 15625 \]
Now let's calculate what the logarithmic function \( g(x) = \log_{25}(x) \) looks like for the point \( (a, 3) \):
The point \( (a, 3) \) means:
\[ g(a) = 3 \]
By definition of the logarithm, this translates to:
\[ \log_{25}(a) = 3 \]
To solve for \( a \), we can rewrite this equation in exponential form:
\[ a = 25^3 \]
Now, we calculate \( 25^3 \):
\[ 25^3 = 15625 \]
Thus, the value of \( a \) is:
\[ \boxed{15625} \]
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