Answer: The correct option is (C) [tex]\dfrac{1}{4}.[/tex]
Step-by-step explanation: We are given to find the value of the following logarithmic expression:
[tex]E=\log_{625}5.[/tex]
We will be using the following logarithmic properties:
[tex](i)~\log_ab=\dfrac{\log b}{\log a},\\\\\\(ii)\log a^b=b\log a.[/tex]
We have
[tex]E\\\\=\log_{625}5\\\\\\=\dfrac{\log 5}{\log 625}\\\\\\=\dfrac{\log5}{\log5^4}\\\\\\=\dfrac{\log5}{4\log 5}\\\\\\=\dfrac{1}{4}.[/tex]
Therefore, the required value of the expression is [tex]\dfrac{1}{4}.[/tex]
thus, (C) is the correct option.
