Question

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

Answer 1

Answer:

The value of $log_{625}(5)$ is $\frac{1}{4}$

Step-by-step 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, $log_{625}(5)=log_{625}(625^{\frac{1}{4}})$

Recall now that,

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

We apply this property to obtain,

$log_{625}(5)=\frac{1}{4}log_{625}(625)$

Recall again that,

$log_a(a)=1,a\ne0\:or\:1$.This implies that,

$log_{625}(5)=\frac{1}{4}(1)$

$log_{625}(5)=\frac{1}{4}$

The correct answer is C.

Answer 2

Answer:

The Answer is C

Step-by-step explanation: