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) $\dfrac{1}{4}.$

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:

$(i)~\log_ab=\dfrac{\log b}{\log a},\\\\\\(ii)\log a^b=b\log a.$

We have

$E\\\\=\log_{625}5\\\\\\=\dfrac{\log 5}{\log 625}\\\\\\=\dfrac{\log5}{\log5^4}\\\\\\=\dfrac{\log5}{4\log 5}\\\\\\=\dfrac{1}{4}.$

Therefore, the required value of the expression is $\dfrac{1}{4}.$

thus, (C) is the correct option.