Question

The logarithmic equation y=log_b x
passes through the point (1/6,−1)
. What is the value of b?

Answer 1

To find the value of \( b \) in the logarithmic equation \( y = \log_b x \) that passes through the point \( \left( \frac{1}{6}, -1 \right) \), we start by substituting the coordinates of the point into the equation.

Given:
\[
x = \frac{1}{6},
\]
\[
y = -1.
\]

Substituting these values into the logarithmic equation gives:
\[
-1 = \log_b \left( \frac{1}{6} \right).
\]

By the definition of logarithms, this equation can be rewritten as:
\[
b^{-1} = \frac{1}{6}.
\]

Taking the reciprocal of both sides, we have:
\[
b = 6.
\]

Thus, the value of \( b \) is \( \boxed{6} \).