Question

if log1/2(x) is greater than or equal to 0 then x belongs to?​

Answer 1

(4−x)≥log

1/2

2−log

1/2

(x−1)

Where, 4−x>0 & x−1>0⇒x∈(1,4)⇒(1)

⇒log

2

(4−x)≤log

2

2−log

2

(x−1)[∵log

a

n

b

m

=

n

m

log

a

b]

⇒log

2

(4−x)≤log

2

x−1

2

[∵loga−logb=log

b

a

]

⇒(4−x)(x−1)≤2

⇒x

2

−5x+6≥0

⇒x≥3 or x≤2⇒(2)

Therefore, using (1) and (2)

x∈(1,2]∪[3,4)

Ans: A,B

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