Answer:
C
Step-by-step explanation:
Use such properties of logarithms:
[tex]\log_w\dfrac{a}{b}=\log_wa-\log_wb,\\ \\\log_wa^b=b\log_wa[/tex]
Thus,
[tex]\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\text{use the first property}=\\ \\=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\\ \\=\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=\text{use the second property}=\\ \\=4\log(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).[/tex]
