Find the exact length of the interval [a,b] for ln^2(x)-2ln(x)-4=0.?

Question

Find the exact length of the interval [a,b] for ln^2(x)-2ln(x)-4=0.

I just need help on it because i don't understand what i need to do.

Answer 1

The interval is a distance between two points.
Let’s find these points.

ln^2(x)-2ln(x)-4=0 or

(ln(x)+1+sqrt(5)) (ln(x)+1-sqrt(5))=0

Solving for x1

ln(x)+1+sqrt(5)=0
ln (x)= -1- sqrt(5)
x1=e^(-1- sqrt(5))

Similarly x2 =e^(-1+ sqrt(5))

The interval is

[e^(-1- sqrt(5)), e^(-1+ sqrt(5))]

Answer 2

1

Answer 3

2

Answer 4

Who cares?