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If `a ,b ,c ,d in R^+-{1},` then the minimum value of `(log)_d a+(log)_b d+(log)_a c+(log)_c b` is `4` `2` `1` none of these``

A

4

B

2

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
A.M `ge`G.M
`implies (log_(4) a + log_(c ) b + log_(a) C + log_(b) d)/(4)`
`ge .^(4)sqrt((log a)/(log d) xx (log_ b)/(log c) xx (log c)/(log a) xx (log d)/(log b))`
or `log_(d) a + log_(b) d + log_(a) c + log_(c ) b ge 4`
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  13. If a ,b ,c ,d in R^+-{1}, then the minimum value of (log)d a+(log)b d...

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  14. If a ,b ,c in R^+, t h e n(b c)/(b+c)+(a c)/(a+c)+(a b)/(a+b) is alwa...

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  15. If a ,b ,c in R^+t h e n(a+b+c)(1/a+1/b+1/c) is always geq12 geq9 lt...

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  16. If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+c...

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  17. If a,b,c,in R^(+), and a,b,c, d are in H.P. then

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  19. f(x)=((x-2)(x-1))/(x-3), forall xgt3. The minimum value of f(x) is equ...

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