Question

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

Answer 1

Answer:

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

Step-by-step explanation:

First use the property of logarithms

$\log _ab-\log_ac=\log_a\dfrac{b}{c}.$

For the given expression you get

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

Now use property of logarithms

$\log_ab^k=k\log_ab.$

For your simplified expression, you get

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