Answer:
C 
Step-by-step explanation:
First use the property of logarithms

For the given expression you get
![\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}}](https://tex.z-dn.net/?f=%5Clog_w%5Cdfrac%7B%28x%5E2-6%29%5E4%7D%7B%5Csqrt%5B3%5D%7Bx%5E2%2B8%7D%20%7D%3D%5Clog_w%28x%5E2-6%29%5E4-%5Clog_w%5Csqrt%5B3%5D%7Bx%5E2%2B8%7D%3D%5Clog_w%28x%5E2-6%29%5E4-%5Clog_w%28x%5E2%2B8%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
Now use property of logarithms

For your simplified expression, you get

Positive turn in too a negative
The two properties are exactly the same when dividing by a positive number. For the division property of equality, dividing by a negative number causes the equal sign to change. Dividing both sides of an inequality by a negative number does not have an effect on the relation symbol.