Answer:
C [tex]4\log_w(x^2-6)-\dfrac{1}{3}\log_w(x^2+8)[/tex]
Step-by-step explanation:
First use the property of logarithms
[tex]\log _ab-\log_ac=\log_a\dfrac{b}{c}.[/tex]
For the given expression you get
[tex]\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\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}}[/tex]
Now use property of logarithms
[tex]\log_ab^k=k\log_ab.[/tex]
For your simplified expression, you get
[tex]\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=4\log_w(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).[/tex]
