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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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