Question

In Exercise, use the properties of logarithms to rewrite the expression as the logarithm of a single quantity.

In x + 4 In y - 1/2 In (z + 4)

Answer 1

ln[xy/sqrt(z+4)]

Explanation:

lnx+ln(y^4)-ln((z+4)^1/2)

The logarithms property states that logxy can be written as log(x)+log(y)

ln(xy)-ln(z+4)^1/2

The logarithms property also states that logx/y can be written as log(x)-log(y)

ln(xy)/ln(z+4)^1/2

ln(xy/(z+4))^1/2

ln[xy/sqrt(z+4)]

Hence by using the logarithms properties In x + 4 In y - 1/2 In (z + 4) can be written as ln[xy/sqrt(z+4)]