Quadratic EquationMedium
Question
If log0.3 (x - 1) < log0.09 (x - 1), then x lies in the interval
Options
A.(2, ∞)
B.(1,2)
C.(-2, -1)
D.None of these
Solution
Given, log0.3 (x - 1) < log0.09(x - 1)
Here , x - 1> 0
⇒ x > 1 and log0.3 (x - 1)<
log0.3 (x - 1)
⇒ x > 1 and log(0.3) (x - 1) < 0
⇒ x > 1 and x > 2
∴ x ∈ (2, ∞)
Here , x - 1> 0
⇒ x > 1 and log0.3 (x - 1)<
log0.3 (x - 1)⇒ x > 1 and log(0.3) (x - 1) < 0
⇒ x > 1 and x > 2
∴ x ∈ (2, ∞)
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