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If loge((a+b)/2)=1/2(loge a+loge b), the...

If `log_e((a+b)/2)=1/2(log_e a+log_e b),` then find the relation between `a and b dot`

Text Solution

Verified by Experts

`log_(e)((a+b)/2)= 1/2 (log_(e)a+log_(e) b)`
` = 1/2 (log_(e)ab) = (log_(e)sqrt(ab))`
` rArr (a+b)/2 = sqrt(ab)`
` or a+b-2sqrt(ab) = 0`
` or (sqrta-sqrtb)^(2)= 0`
`or a = b`
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