Question

Exam for advanced algebra

Answer 1

The correct answer is option 3

2log₅x - 2 log₅4

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 2

third option

Explanation:

Using the laws of logarithms

•
`log_(b)`(
`x^(n)`) ⇒ n
`log_(b)` x

• log (
`(x)/(y)`) ⇒ log x - log y

Hence

2
`log_(5)`(
`(x)/(4)`)

= 2(
`log_(5)` x -
`log_(5)` 4 )

= 2
`log_(5)` x - 2
`log_(5)` 4