Question

Please help me on this

Answer 1

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

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}=(1)/(3) log_(w) (x^(2)+8)`

∴
`4log_(w)(x^(2)-6)-(1)/(3)log_(w)(x^(2)+8)`

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