# The inequality ln ( x 2 − 2 x − 2 ) ≤ 0 .

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1, Problem 13P
To determine

## To solve: The inequality ln(x2−2x−2)≤0.

Expert Solution

Solution:

The solution is x[1,13)(1+3,3]x[1,13)(1+3,3].

### Explanation of Solution

Given:

The inequality: ln(x22x2)0.

Calculation:

Consider the inequality ln(x22x2)0.

The inequality is not possible as ln(x22x2) value is always positive.

That is, ln(x22x2)>0.

Obtain the root of (x22x2)

x=2±4+82=2±4(3)2=1±3

Thus the intervals are follows,

x(,13)(1+3,) (1)

Then the inequality,

ln(x22x2)0x22x21x22x30(x3)(x+1)0

The roots are x=3 and x=1

Thus, the interval as follows,

x[1,3] (2)

Thus, from the equation (1) and equation (2), it can be concluded that,

x[1,13)(1+3,3]

Therefore, the solution is x[1,13)(1+3,3].

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