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First, we need to use this radical property:
sqrt(x) = x^1/2
So then we would have:
ln( sqrt(ab) ) = ln( (ab)^1/2 )
After this, we use this logaritmic property:
ln(x^n) = n*ln(x)
So it will be like this:
ln( (ab)^1/2 ) = 1/2ln(ab)
Then we use this logaritmic property:
ln(xy) = ln(x) + ln(y)
So we would have the following:
1/2ln(ab) = 1/2( ln(a) + ln(b) ) = 1/2ln(a) + 1/2ln(b)
Final answer: 1/2ln(a) + 1/2ln(b)
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