Cj 1.

asked • 05/27/17

[x^2-4]÷[log1/2(x^2-1) <0 1/2 is the base here

Logarithmic inequalities

Kris V.

All logb1 = 0 where b > 0 and b ≠ 1
log½x = -log2x, so log½(x2-1) < 0 for x2-1 >1 ⇒ x < -√2 or x > √2
x2 -4 >0 for x < -2 or x >2.
 
I think the answer should be x < -2 or x >2 (where x2 -4 >0 and log½(x2-1) < 0)
 
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05/28/17

Kris V.

Additional choices for x
log½(x2-1) > 0 ⇒ 0 < x2-1 < 1 or 1 < x2 < 2 ⇒ 1 < |x| < √2
x2 - 4 < 0 ⇒ |x| < 2
 The solution should be 1 < |x| < √2 or |x| > 2
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05/28/17

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