Respuesta :

imlittlestar

Answer:

The correct answer is option 3

2log₅x - 2 log₅4

Step-by-step explanation:

Points to remember

1). logₐ(x/y) = logₐx - logₐy

2). logₐx² = 2logₐx

From the above we can write,

log₅(x/4)² = 2log₅(x/4)

= 2[log₅(x/4)] = 2[ log₅x - log₅4]

= 2log₅x -2 log₅4]

From the given expression we get the correct answer is option 3

2log₅x - 2 log₅4

Answer:

third option

Step-by-step explanation:

Using the laws of logarithms

• [tex]log_{b}[/tex]([tex]x^{n}[/tex]) ⇒ n [tex]log_{b}[/tex] x

• log ([tex]\frac{x}{y}[/tex]) ⇒ log x - log y

Hence

2 [tex]log_{5}[/tex]([tex]\frac{x}{4}[/tex])

= 2([tex]log_{5}[/tex] x - [tex]log_{5}[/tex] 4 )

= 2[tex]log_{5}[/tex] x - 2[tex]log_{5}[/tex] 4