To find the value of \( b \) in the logarithmic equation \( y = \log_b x \) that passes through the point \( (16, -1) \), we can substitute the values of \( x \) and \( y \) from the point into the equation.
Given the point \( (16, -1) \):
\[ y = -1 \quad \text{and} \quad x = 16 \]
Substituting into the equation gives us:
\[ -1 = \log_b(16) \]
Using the definition of logarithms, we can rewrite this as:
\[ b^{-1} = 16 \]
This implies
\[ \frac{1}{b} = 16 \]
To find \( b \), we can take the reciprocal of both sides:
\[ b = \frac{1}{16} \]
Thus, the value of \( b \) is
\[ \boxed{\frac{1}{16}} \]