What is log_{2}(|x-2|)>log_{2}(|x+4|) ?

The solution to log_{2}(|x-2|)>log_{2}(|x+4|) is x<-4\lor-4<x<-1

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log_{2}(|x-2|)>log_{2}(|x+4|)

lo g_{2} (∣ x - 2 ∣) > lo g_{2} (∣ x + 4 ∣)

x < - 4 or - 4 < x < - 1

Solution steps

lo g_{2} (∣ x - 2 ∣) > lo g_{2} (∣ x + 4 ∣)

Find positive and negative intervals

x < - 4, - 4 \leq x < 2, x \geq 2

Solve the inequality for each interval

x < - 4 or - 4 < x < - 1 or No Solution

Merge Overlapping Intervals

x < - 4 or - 4 < x < - 1

∣ x + 1 ∣^{2} + 2 ∣ x + 2 ∣ \geq 2

x^{2} - 2 x + ∣ x - 4 ∣ < x^{2} - 3 x + 4

∣ - 6 (n + 5) ∣ > - 12

x^{2} - x - 6 < 6

∣ x - 1 ∣ + ∣ x - 2 ∣ < 7

What is log_{2}(|x-2|)>log_{2}(|x+4|) ?
The solution to log_{2}(|x-2|)>log_{2}(|x+4|) is x<-4\lor-4<x<-1