Use the Laws of Logarithms to expand the expression. ln ab

Algebra
Tutor: None Selected Time limit: 1 Day

Use the Laws of Logarithms to expand the expression.
ln 
SQRTab
Jul 17th, 2015

Thank you for the opportunity to help you with your question!

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)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 17th, 2015

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