Question

Which expression is equivalent to log w (x^2 -6)^4/ 3 sqrt x^2+8?

Answer 1

Answer: C

Explanation:

Answer 2

C
`4\log_w(x^2-6)-(1)/(3)\log_w(x^2+8)`

Explanation:

First use the property of logarithms

`\log _ab-\log_ac=\log_a(b)/(c).`

For the given expression you get

`\log_w\frac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\log_w(x^2-6)^4-\log_w(x^2+8)^{(1)/(3)}`

Now use property of logarithms

`\log_ab^k=k\log_ab.`

For your simplified expression, you get

`\log_w(x^2-6)^4-\log_w(x^2+8)^{(1)/(3)}=4\log_w(x^2-6)-(1)/(3)\log_w(x^2+8).`