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Question: If log<sub>0.3</sub> (x – 1) \< log<sub>0.09</sub> (x – 1), then x lies in the interval -...

If log0.3 (x – 1) < log0.09 (x – 1), then x lies in the interval -

A

(2, ¥)

B

(1, 2)

C

(–2, –1)

D

None of these

Answer

(2, ¥)

Explanation

Solution

log0.3 (x – 1) < log(0.3)2 (x – 1)

̃ log0.3 (x – 1) < 12\frac{1}{2} log0.3 (x – 1)

̃ log0.3 (x – 1)2 < log0.3 (x – 1)

(x – 1)2 > (x – 1)

(x – 1) (x – 2) > 0 ̃ x < 1 or x > 2

But log (x – 1) is defined if x – 1 > 0 ̃ x > 1

Common value is x > 2 ̃ (2, ¥)