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If a > 1, b > 1 , then the minimum val...

If a > 1, b > 1 , then the minimum value of `log_b a+ log_a b` is :

A

0

B

1

C

2

D

none of

Text Solution

Verified by Experts

The correct Answer is:
C
Using `A.M.geG.M.,` wc have
`(log_(b)a+log_(a)b)/(2)gesqrt(log_(b)alog_(a)b)`
`impliescos^(3)theta+sec^(3)thetage2.`
Hence, the minimum value of `log_(b)a+log_(a)b` is 2 and it is attained when a=b.
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