Question

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

Answer 1

log
0.3
​
(x−1)0.09
​
(x−1)

Upon applying log rules, we get,

log
0.3
​
(x−1)0.3
​
(
x−1
​
)

⇒x−1>
x−1
​
and

x−1
​
>0

Now,

x−1>
x−1
​


(
x−1
​
)
2
<(x−1)
2


x−12
−2x+1

x<1orx>2

Now,

x−1≥0:x≥1

Overlapping all the intervals, we get,

x>2


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