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)

ln[xy/sqrt (z+4) ]

Step-by-step 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) ]