Question

URGENT WILL GIVE BRAINLIEST 

Answer 1

Answer:

C. $4\cdot log_w(x^2-6)-\frac{1}{3}\cdot log_w((x^2+8)$

Step-by-step explanation:

We have been given an expression $log_w\frac{(x^2-6)^4}{\sqrt[3]{x^2+8}}$. We are asked to choose the equivalent expression to our given expression.  

Upon applying log rule $log_c(\frac{a}{b})=log_c(a)-log_c(b)$, we will get:

$log_w(x^2-6)^4-log_w(\sqrt[3]{x^2+8})$

Using exponent rule $\sqrt[n]{x}=x^{\frac{1}{n}}$, we will get:

$log_w(x^2-6)^4-log_w((x^2+8)^{\frac{1}{3}}$

Now, we will apply rule $log_c(a^b)=b\cdot log_c(a)$ to simplify our expression as:

$4\cdot log_w(x^2-6)-\frac{1}{3}\cdot log_w((x^2+8)$

Therefore, option C is the correct choice.

Answer 2

Answer:

C.

Step-by-step explanation:

This can be written as

$log_w\frac{(x^2-6)^4}{(x^2+8)^\frac{1}{3} }$

when you divide log you should subtract the terms

$log_w(x^2-6)^4-log_w(x^2+8)^\frac{1}{3}$

Rewrite powers in the terms as below

$4log_w(x^2-6)-\frac{1}{3} log_w(x^2+8)$