If a,b,c,d in R^(+)-{1}, then the minimu...

If `a,b,c,d in R^(+)-{1}`, then the minimum value of `log_(d) a+ log_(c)b+log _(a)c+log_(b)d` is

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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