condense the expression. ln 4xy^2 - 2 ln x^2 y

Question

I don't know how to condense ln expressions.

Answer 1

x^a * x^b = x^a+b , x^a / x^b = x^a-b , (x^a)^b = x^ab , x⁰ = 1
~~~~~~~~~~~~~
ln 4xy² - 2 ln x² y = ln   4xy² -  ln (x²y)² =
                                             ↓        ↓
                                             ↓  ln  x⁴y²  
                                             ↓  
                                ln ((4xy²) / (x⁴y²)) = ln 4x^-3  or  (ln 4 - 3 ln x)
                                                  

Answer 2

To condense is the opposite of to expand. Here you use properties of logarithms.

ln(4xy²) - 2ln(x²y) = ln(4xy²) - ln( (x²y)² ) = ln(4xy²) - ln(x⁴y² ) =

= ln[(4xy²)/(x⁴y²)] = ln(4/x³)

That's it! Make sure you know which property was used at each step...

Hope it helps!