Question

What is the value of log625^5? A: -4 B:-1/4 C:1/4 D:4

Answer 1

The Answer is C

Explanation:

Answer 2

The value of
`log_(625)(5)` is
`(1)/(4)`

Explanation:

We want to evaluate
`log_(625)(5)`.

The base of this logarithm is
`625` and the number is
`5`.

We need to express the number
`5` as the base
`625` raised to a certain index.

This implies that,
`log_(625)(5)=log_(625)(625^{(1)/(4)})`

Recall now that,

`log_a(m^n)=nlog_a(m)`.

We apply this property to obtain,

`log_(625)(5)=(1)/(4)log_(625)(625)`

Recall again that,

`log_a(a)=1,a\\e0\:or\:1`.This implies that,

`log_(625)(5)=(1)/(4)(1)`

`log_(625)(5)=(1)/(4)`

The correct answer is C.