Condensing logarithms?

Question

how do you do these??

1.(1/2){ln (x^2) - ln y^4}
2.ln c - 2ln d

Answer 1

1. 1/2 (2 ln x - 4 ln) [Using the Laws of logarithm]
= ln x - 2ln y [Opening the brackets]
= ln x - ln y^2
= ln (x/y^2)

2. ln c - ln d^2
= ln (c/d^2)


You may look for Laws of Logarithm on http://en.wikipedia.org/wiki/Logarithmic_identities

Hope this helps.

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Answer 2

1. ln (x/y^4)
2. ln (c/d^2)

Answer 3

1/2*ln(x^2) - ln(y^4) = 1/2*2*ln(x) - 4ln(y) = ln(x)-4ln(y) = ln(x/y^4)

ln c -2 ln d = ln(c/d^2)