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

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

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

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 logarithmic and exponential functions. Specifically, if \( f(x) = a^b \) then \( g(x) = \log_a(b) \).

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

\[ 9^2 = 81 \]

This means:

• \( x = 2 \) corresponds to \( f(2) = 81 \)
• We can express this point in the context of the logarithmic function as follows:

Since \( g(81) = \log_9(81) \), we need to find what \( g(81) \) equals. The relationship means:

\[ \log_9(81) = 2 \]

This indicates that the point \( (81, 2) \) lies on the graph of the logarithmic function \( g(x) \).

Therefore, the correct response is:

(81, 2)