# If x is satisfied the inequality #log_(x+3)(x^2-x) < 1#, the x may belongs to the set?

##
A) #x in (-3,-2)#

B) #x in (-1,3)#

C) #x in (1,3)#

D) #x in (-1,0)#

The answer is A), C) and D) for your reference

A)

B)

C)

D)

The answer is A), C) and D) for your reference

##### 1 Answer

I got

#### Explanation:

By the definition of the logarithm, we have:

#x^2 - x < (x + 3)^1#

#x^2 - x < x + 3#

#x^2 - 2x - 3 < 0#

Solving like an equation:

#x^2 - 2x - 3 = 0#

#(x- 3)(x + 1) = 0#

#x= 3 or -1#

If we select a test point, say

#0^2 - 2(0) - 3 < 0 color(green)(√)#

However, if we use

#x^2 - x > 0#

#x^2 - x = 0#

#x(x - 1) = 0#

#x = 0 or 1#

If we repeat the process with test points, we realize that the solution is

Now, we must also guarantee that

The answer is therefore :

#x in (-3, -2) uu (-1, 0) uu (0, 3)#

A graphical verification yields the same results.

Hopefully this helps!