Respuesta :

semsee45

Answer:

[tex]\textsf{D)}\quad \log_x 8[/tex]

Step-by-step explanation:

Given logarithmic expression:

[tex]5\log_x 2-\log_x 4[/tex]

To simplify the given expression, we can use logarithmic properties.

[tex]\boxed{\begin{array}{rl}\underline{\sf Logarithm\;Rules}\\\\\sf Power:&\log_ax^n=n\log_ax\\\\\sf Quotient:&\log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay\end{array}}[/tex]

Begin by applying the power rule of logarithms:

[tex]\log_x 2^5 -\log_x 4[/tex]

[tex]\log_x 32 -\log_x 4[/tex]

Now, apply the quotient rule of logarithms:

[tex]\log_x\left(\dfrac{32}{4}\right)[/tex]

[tex]\log_x 8[/tex]

Therefore, the equivalent expression to 5 logₓ 2 - logₓ 4 is:

[tex]\huge\boxed{\boxed{\log_x 8}}[/tex]

msm555

Answer:

D: [tex] \log_x 8 [/tex]

Step-by-step explanation:

To find the equivalent expression for [tex]5 \log_x 2 - \log_x 4[/tex], we can use logarithmic properties. The key property here is the division rule for logarithms:

[tex] \log_a \dfrac{b}{c} = \log_a b - \log_a c [/tex]

Applying this property to the given expression:

[tex] 5 \log_x 2 - \log_x 4 = \log_x 2^5 - \log_x 4 [/tex]

Now, [tex]2^5[/tex] is equal to 32, so we can rewrite the expression as:

[tex] \log_x 32 - \log_x 4 [/tex]

Now, using the division rule for logarithms:

[tex] \log_x \dfrac{32}{4} [/tex]

Simplifying further, [tex] \dfrac{32}{4} = 8[/tex]:

[tex] \log_x 8 [/tex]

So, the equivalent expression is [tex] \log_x 8 [/tex], which corresponds to:

D: [tex] \log_x 8 [/tex]