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abs(x² - 4)^(x² - x - 6) < 1

here's my work:

1. taking the log of both sides (can i do this even if it's an inequality?)

log (abs(x² - 4)^(x² - x - 6)) < log 1

which is

(x² - x - 6)*(log(abs(x² - 4))) < 0

2. I can then say:

(x² - x - 6) < 0

OR

log(abs(x² - 4)) < 0

3. Solving:

(x² - x - 6) < 0

gives: -2 < x < 3

log(abs(x² - 4)) < 0

gives: -sqrt(5) < x < -sqrt(3) and sqrt(3) < x < sqrt(5)

so the solution set is:

]-√5 , -2[ U ]√5 , 3[ U ]-√3,√3[

Questions:

1. Is my work correct?

2. How would you do it, and can you please show work?

Thank you

EDIT: It's not really a homework... I was just wondering how would you guys do it :S

Sorry

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# Solving this inequation

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