Question

Please help me on this

Answer 1

Answer:

The answer is expression 4㏒w(x² - 6) - (1/3)㏒w(x² + 8) ⇒ 3rd answer

Step-by-step explanation:

* Lets revise some rules of the logarithmic functions  

- log(a^n) = n log(a)

-  log(a) + log(b) = log(ab) ⇒ vice versa  

- log(a) - log(b) = log(a/b)  ⇒ vice versa

* Lets solve the problem

- The expression is

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

∵ log(a/b) = log(a) - log(b)

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

∵ ∛(x² + 8) can be written as (x² + 8)^(1/3)

∵ log(a^n) = n log(a)

∴ $log_{w}(x^{2}-6)^{4}=4log_{w}(x^{2}-6)$

∴ $log_{w}\sqrt[3]{x^{2}+8}=\frac{1}{3} log_{w} (x^{2}+8)$

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

* The answer is expression 4㏒w(x² - 6) - (1/3)㏒w(x² + 8)