Respuesta :

ShyzaSling

Answer:

option C

[tex]log_{w}4(x^{2}-6)}-\frac{1}{3} ({x^{2}+8)}[/tex]

Step-by-step explanation:

Given in the question an expression

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

Step1

Apply logarithm subtraction rule:

[tex]log_{w}\frac{m}{n}=log_{w}m-n[/tex]

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

Step2

Apply logarithm power rule

[tex]log_{w}x^{n}=nlog_{w}x[/tex]

[tex]log_{w}4(x^{2}-6)}-\frac{1}{3} ({x^{2}+8)}[/tex]

as

[tex]\sqrt[n]{x}=(x)^\frac{1}{n}[/tex]

kudzordzifrancis

Answer:

C. [tex]4\log_w(x^2-6)-\frac{1}{3} \log_w(x^2+8)[/tex]

Step-by-step explanation:

The given logarithmic expression is

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

Recall and use the quotient law of logarithms;

[tex]\log_a(\frac{m}{n} )=\log_a(m )-\log_a(n)[/tex]

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

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

Recall and use the power rule of logarithms:[tex]\log_aM^n=n\log_aM[/tex]

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

The correct choice is C.

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