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Question

If a,b,c+R , then the minimum value of alogblogc+blogcloga+clogalogb is

A
3
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B
1
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C
9
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D
16
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Solution

The correct option is B 3
We know that A.M.G.M.

alogblogc+blogcloga+clogalogb33alogblogc×blogcloga×clogalogb

alogblogc+blogcloga+clogalogb33alogbalogc×blogcbloga×clogaclogb

alogblogc+blogcloga+clogalogb33alogbalogc×blogcalogb×alogcblogc (since, alogb=bloga)

alogblogc+blogcloga+clogalogb331

alogblogc+blogcloga+clogalogb3

Therefore, the minimum value of alogblogc+blogcloga+clogalogb is 3

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