Which of the following is/are true, For f(x)=ln(lnx)lnx
A
(ln 2.1)ln2.2 > (ln 2.2)ln2.1
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B
(ln 4)ln5 < (ln5)ln4
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C
(ln30)ln31 < (ln31)ln30
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D
(ln28)ln30 < (ln30)ln28
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Solution
The correct option is B (ln 4)ln5 < (ln5)ln4 Let f(x) = ln(lnx)lnx f'(x)= 1−ln(lnx)x(lnx)2<0∀x>ee So f(x) is increasing in (1, ee) and decreasing in (ee,∞) So x >y⇒(lnx)lny<(lny)lnx∀x,yϵ(ee,∞) and x <y⇒(lnx)lny<(lny)lnx∀x,yϵ(1,ee)