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
[tex]log_{w}\frac{(x^{2}-6)^{4}}{\sqrt[3]{x^{2}+8}}[/tex]
∵ log(a/b) = log(a) - log(b)
∴ [tex]log_{w}(x^{2}-6)^{4}-log_{w}\sqrt[3]{x^{2}+8}[/tex]
∵ ∛(x² + 8) can be written as (x² + 8)^(1/3)
∵ log(a^n) = n log(a)
∴ [tex]log_{w}(x^{2}-6)^{4}=4log_{w}(x^{2}-6)[/tex]
∴ [tex]log_{w}\sqrt[3]{x^{2}+8}=\frac{1}{3} log_{w} (x^{2}+8)[/tex]
∴ [tex]4log_{w}(x^{2}-6)-\frac{1}{3}log_{w}(x^{2}+8)[/tex]
* The answer is expression 4㏒w(x² - 6) - (1/3)㏒w(x² + 8)
