expand : log (√(ab)/e^2)

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We have to expand log (sqrt (ab)/e^2). I assume the base of the logarithm here is e.

log(e) [(sqrt (ab)/e^2)]

We use the relations log ab = log a + log b, log a/b = log a - log b and log x^n = n*log x

=> log(e) [sqrt (ab)] - log(e) e^2

=> (1/2)*log(e) [ ab] - 2*log(e) e

=> (1/2)*log(e) a - (1/2)*log(e) b - 2

The required result is (1/2)*log(e) a - (1/2)*log(e) b - 2

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