Question

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

Answer 1

Using change of base
log5/log 625
both logs cancels
then becomes 5/625
+ 1/4

Answer 2

Answer: The correct option is (C)
`(1)/(4).`

Step-by-step explanation: We are given to find the value of the following logarithmic expression:

`E=\log_(625)5.`

We will be using the following logarithmic properties:

`(i)~\log_ab=(\log b)/(\log a),\\\\\\(ii)\log a^b=b\log a.`

We have

`E\\\\=\log_(625)5\\\\\\=(\log 5)/(\log 625)\\\\\\=(\log5)/(\log5^4)\\\\\\=(\log5)/(4\log 5)\\\\\\=(1)/(4).`

Therefore, the required value of the expression is
`(1)/(4).`

thus, (C) is the correct option.