Answer: ln(2)
Step-by-step explanation:
In order to minimize ln[(x – 3)^2 + 2], we have to minimize [(x – 3)^2 + 2] since natural log is an increasing function
For that, it suffices to minimize (x – 3)^2, which is non-negative for all real numbers x
As such, the minimum value is achieved when x - 3 = 0; - 5 < 3 < 5
Substitute x = 3 in the original equation to get ln(2)
