Question

Question 7 of 10Use the properties of logarithms to expand the following expression.(√log(x+4)5x³Your answer should not have radicals or exponents.You may assume that all variables are positive.

Answer 1

We have:

`\begin{gathered} log(\sqrt{((x+4)^5)/(x^3)}) \\ =log(((x+4)^2√(x+4))/(x√(x)) \end{gathered}`

Applying properties of logarithms:

`\begin{gathered} =log((x+4)^2√(x+4))-log(x√(x)) \\ =2log(x+4)+log(√(x+4))-logx-log√(x) \end{gathered}`