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

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

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

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

(1,0)

Answer 1

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

Given that \( f(x) = 9^x \) includes the point \( (2, 81) \), we can express this as:

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

Now, the logarithmic function \( g(x) = \log_9 x \) gives us the relationship where:

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

Since \( 81 \) can be rewritten as \( 9^2 \), we find:

\[ g(81) = \log_9 (9^2) = 2 \]

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

So, the correct response is:

\[ \text{(81, 2)} \]