Question

The graphs of
y
=
3
x
and
y
=
(
1
3
)
x
are shown below.

image.png
2026_03_02_02_45_333.png
What is the solution to the inequality
(
1
3
)
x
<
3
x
according to the graph?


x
<
1


x
<
0


x
>
1


x
>
0

Answer 1

(1/3)^x = 3^{-x}, so the inequality 3^{-x} < 3^{x} gives -x < x, hence 0 < 2x and x > 0.

Answer: x > 0.