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

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

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

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

(2,81)

Answer 1

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

Given the point (2, 81) on the graph of the exponential function \( f(x) = 9^x \), we have:

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

Now, since the logarithm is the inverse of the exponential function, the point \( (x, y) \) that corresponds to \( (2, 81) \) in the logarithmic function is given by:

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

Thus, the corresponding point on the graph of the logarithmic function \( g(x) \) is \( (81, 2) \).

Therefore, the correct answer is:

(81, 2)