Question
If the exponential function f(x)=7x includes the point (2,49) on the graph of the exponential curve, which point can be described as lying on the graph of the logarithmic function g(x)=log7x ?(1 point) Responses (49,2) open paren 49 comma 2 close paren (2,49) open paren 2 comma 49 close paren (1,7) open paren 1 comma 7 close paren (1,0)
Answers
GPT-4o mini
To find a point on the graph of the logarithmic function \( g(x) = \log_7 x \) based on the given point on the exponential function \( f(x) = 7^x \), we can use the relationship between logarithmic and exponential functions.
Recall that if \( f(a) = b \), then \( g(b) = a \). In this case, we have:
\[
f(2) = 7^2 = 49
\]
This means that \( g(49) = 2 \). Therefore, the point that lies on the graph of the logarithmic function \( g(x) = \log_7 x \) is \( (49, 2) \).
So, the correct answer is:
**(49, 2)**
Recall that if \( f(a) = b \), then \( g(b) = a \). In this case, we have:
\[
f(2) = 7^2 = 49
\]
This means that \( g(49) = 2 \). Therefore, the point that lies on the graph of the logarithmic function \( g(x) = \log_7 x \) is \( (49, 2) \).
So, the correct answer is:
**(49, 2)**