fx ln x3 and gx x Find the intervals when fx gx No algebr

f(x) = ln x3 and g(x) = x. Find the intervals when f(x) < g(x). No algebra involved. Use calcualtor zero or root method only.

Solution

ln(x^3) < x

3ln(x) < x

On a calculator, we get ln(x^3) > x for all x in (1.857 , 4.536)

So, for ln(x^3) < x, it would be :

(0 , 1.857) U (4.536 , inf) ----> ANSWER