Question

If the exponential function f(x)=9x
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

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

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

(1,0)
left parenthesis 0 comma 1 right parenthesis

(81,2)

Answer 1

To find a point that lies on the graph of the logarithmic function \( g(x) = \log_9 x \), we can use the relationship between exponential functions and their corresponding logarithmic functions.

The exponential function \( f(x) = 9^x \) includes the point \( (2, 81) \), meaning that:

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

In logarithmic terms, the definition of logarithm states that if \( f(a) = b \), then \( g(b) = a \). In this case, since \( 9^2 = 81 \), we have:

\[
g(81) = \log_9 81 = 2
\]

Thus, the point \( (81, 2) \) lies on the graph of the logarithmic function \( g(x) = \log_9 x \).

Therefore, the correct answer is:

**(81, 2)**