Question

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 is 3^{-x} < 3^{x}. Since 3^t is increasing, this is equivalent to -x < x, i.e. 2x > 0 → x > 0.

Answer: x > 0.