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if log_0.3(x-1) < log_0.09(x-1) , then x lies in the interval

if log_0.3(x-1) < log_0.09(x-1) , then x lies in the interval

Grade:12

2 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
for base less than 1
log is decreasing function so
(x-1) > (x-1)^(-0.5)
=>(x-1)(x-2) >0
=> x belongs to (-infinity,1) or (2,infinity)
Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
also if let's assume x belongs to (1,2)
then (x-1)^2 < (x-1)
=> (x-2)(x-1)<0
=> x belongs to (1,2) too

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