MATH SOLVE

10 months ago

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

Accepted Solution

A:

Answer:The value of [tex]log_{625}(5)[/tex] is [tex]\frac{1}{4}[/tex]Step-by-step explanation:We want to evaluate [tex]log_{625}(5)[/tex].

The base of this logarithm is [tex]625[/tex] and the number is [tex]5[/tex].

We need to express the number [tex]5[/tex] as the base [tex]625[/tex] raised to a certain index.

This implies that, [tex]log_{625}(5)=log_{625}(625^{\frac{1}{4}})[/tex]

Recall now that,[tex]log_a(m^n)=nlog_a(m)[/tex].

We apply this property to obtain,[tex]log_{625}(5)=\frac{1}{4}log_{625}(625)[/tex]

Recall again that,

[tex]log_a(a)=1,a\ne0\:or\:1[/tex].This implies that,

[tex]log_{625}(5)=\frac{1}{4}(1)[/tex]

[tex]log_{625}(5)=\frac{1}{4}[/tex]

The correct answer is C.

The base of this logarithm is [tex]625[/tex] and the number is [tex]5[/tex].

We need to express the number [tex]5[/tex] as the base [tex]625[/tex] raised to a certain index.

This implies that, [tex]log_{625}(5)=log_{625}(625^{\frac{1}{4}})[/tex]

Recall now that,[tex]log_a(m^n)=nlog_a(m)[/tex].

We apply this property to obtain,[tex]log_{625}(5)=\frac{1}{4}log_{625}(625)[/tex]

Recall again that,

[tex]log_a(a)=1,a\ne0\:or\:1[/tex].This implies that,

[tex]log_{625}(5)=\frac{1}{4}(1)[/tex]

[tex]log_{625}(5)=\frac{1}{4}[/tex]

The correct answer is C.