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Question

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


A

2,

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B

1,2

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C

-2,-1

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D

None of these

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Solution

The correct option is A

2,


Explanation for the correct option.

Step 1: Simplify the given inequality.

log0.3(x-1)<log0.09(x-1)log0.3(x-1)<log0.32(x-1)log0.3(x-1)<12log0.3(x-1)2log0.3(x-1)<log0.3(x-1)log0.3(x-1)2<log0.3(x-1)

Step 2: Apply log rule.

We know that if logba<logbc, where 0<b<1, then a>c. So here we can say that,

x-12>x-1x2-2x+1>x-1x2-3x+2>0x-1x-2>0

Step 3: Find the interval of x.

From x-1x-2>0 we get x1,2,, therefore, x lies in 2,.

Hence, option A is correct.


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