Question

The logarithmic equation y=logbx
passes through the point (16,−1)
. What is the value of b?(1 point)
b=

Answer 1

To find the value of \( b \) in the equation \( y = \log_b x \) given that it passes through the point \( (16, -1) \), we will substitute \( x = 16 \) and \( y = -1 \) into the equation.

Starting with the equation:

\[
-1 = \log_b 16
\]

This can be rewritten in its exponential form:

\[
b^{-1} = 16
\]

Which can be rearranged to:

\[
\frac{1}{b} = 16
\]

Now, we can solve for \( b \) by taking the reciprocal of both sides:

\[
b = \frac{1}{16}
\]

Thus, the value of \( b \) is:

\[
\boxed{\frac{1}{16}}
\]