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

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2 Answers

xa * xb = xa+b , xa / xb = xa-b , (xa)b = xab , 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)
                                                  

Comments

-3 ln (4x) = ln (4x)^-3  = ln(1/((4^3)(x^3) ?  ln(4x^-3)

You are right George, thank you :-)

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!