Write In (4/9) in terms of In 2 and In 3. A)21n 2 - 21n 3
B)4In 2 - 4In 3
C) 3(In 2 - In 3)
D)In2 2 - 4In 3

Answer

A) 2 ln 2 - 2 ln 3

Explanation

Using the laws of logarithms:

ln (x/y) = ln (x) - ln (y)

ln (4/9) = ln (4) - ln (9)

This can be written as

ln (2^2) - ln (3^2)

Another law is:

ln (n^m) = m ln(n)

So finally:

2ln (2) - 2ln 3