Question

The point (625,4)
lies on the graph of f(x) =log_5 x
. What is the corresponding point on the graph of g(x) = 5^x
?



A
(−625,−4)\left(-625,-4\right)(−625,−4)

B
(4,625)\left(4,625\right)(4,625)

C
(4,−625)\left(4,-625\right)(4,−625)

D
(625,4)\left(625,4\right)(625,4)

Answer 1

Given that the point \((625, 4)\) lies on the graph of \(f(x) = \log_5 x\), this means that:

\[
f(625) = 4 \implies \log_5(625) = 4
\]

This implies:

\[
5^4 = 625
\]

We want to find the corresponding point on the graph of \(g(x) = 5^x\). The x-coordinate from \(f(x)\) becomes the y-coordinate in \(g(x)\), and the output of \(f(x)\) becomes the input for \(g(x)\):

\[
g(4) = 5^4 = 625
\]

Thus, the corresponding point on the graph of \(g(x)\) is:

\[
(4, 625)
\]

Therefore, the answer is:

**B (4, 625)**