Question

Compare the functions f(x)=8x
and g(x)=log8x
. The graph of f(x)
contains the points (1,8)
and (−1,0.125)
. Select the answer choice that contains two points on the graph of g(x)
.

Answer 1

To compare the functions \( f(x) = 8x \) and \( g(x) = \log_8(x) \), we should find some points on the graph of \( g(x) \).

First, let's derive a couple of points for \( g(x) \).

1. **Choose \( x = 1 \):**

\[
g(1) = \log_8(1)
\]
Since any logarithm of 1 is 0, we have:
\[
g(1) = 0
\]

So, one point on the graph of \( g(x) \) is \( (1, 0) \).

2. **Choose \( x = 8 \):**

\[
g(8) = \log_8(8)
\]
Since \( 8^1 = 8 \), we have:
\[
g(8) = 1
\]

So, another point on the graph of \( g(x) \) is \( (8, 1) \).

Now, we have two points on the graph of \( g(x) \):
- \( (1, 0) \)
- \( (8, 1) \)

Based on this comparison, we can conclude that the points \( (1, 0) \) and \( (8, 1) \) are two points on the graph of \( g(x) = \log_8(x) \).