Answer:
C. [tex]4\cdot log_w(x^2-6)-\frac{1}{3}\cdot log_w((x^2+8)[/tex]
Step-by-step explanation:
We have been given an expression [tex]log_w\frac{(x^2-6)^4}{\sqrt[3]{x^2+8}}[/tex]. We are asked to choose the equivalent expression to our given expression.
Upon applying log rule [tex]log_c(\frac{a}{b})=log_c(a)-log_c(b)[/tex], we will get:
[tex]log_w(x^2-6)^4-log_w(\sqrt[3]{x^2+8})[/tex]
Using exponent rule [tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex], we will get:
[tex]log_w(x^2-6)^4-log_w((x^2+8)^{\frac{1}{3}}[/tex]
Now, we will apply rule [tex]log_c(a^b)=b\cdot log_c(a)[/tex] to simplify our expression as:
[tex]4\cdot log_w(x^2-6)-\frac{1}{3}\cdot log_w((x^2+8)[/tex]
Therefore, option C is the correct choice.
