If the exponential function f(x)=9x

Question

includes the point (2,81)
on the graph of the exponential curve, which point can be described as lying on the graph of the logarithmic function g(x)=log9x
?(1 point)
Responses

(81,2)
left parenthesis 81 comma 2 right parenthesis

(2,81)
left parenthesis 2 comma 81 right parenthesis

(1,9)
left parenthesis 1 comma 9 right parenthesis

(1,0)

Answer 1

To determine which point lies on the graph of the logarithmic function \( g(x) = \log_9 x \), we can use the fact that \( g(x) \) is the inverse of \( f(x) \).

Since \( f(x) = 9^x \) and the point \( (2, 81) \) lies on the graph of \( f(x) \), we have:

\[ f(2) = 9^2 = 81 \]

This means that for the logarithmic function \( g(x) = \log_9 x \), if \( f(2) = 81 \), then:

\[ g(81) = 2 \]

Thus, the point \( (81, 2) \) lies on the graph of \( g(x) \).

Therefore, the correct response is:

(81, 2)