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

2 Answers

4 votes

Answer:

The Answer is C

Explanation:

User Arakweker
by
7.2k points
1 vote

Answer:

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.



User Bryan Oemar
by
8.0k points

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