To find the value of \( a \) such that the point \( (a, 3) \) is on the logarithmic function \( g(x) = \log_{25}(x) \), we start by using the fact that the \( y \)-coordinate of this point is \( 3 \).
This leads to the equation: \[ g(a) = \log_{25}(a) = 3 \]
To solve for \( a \), we can convert the logarithmic equation to its exponential form: \[ a = 25^3 \]
Now we calculate \( 25^3 \): \[ 25^3 = (5^2)^3 = 5^{2 \cdot 3} = 5^6 \] Calculating \( 5^6 \): \[ 5^6 = 15625 \]
Thus, the value of \( a \) is: \[ \boxed{15625} \]
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