Answer: The value is \(\dfrac{1}{4}.\)
Step-by-step explanation: We are given to find the value of the following logarithmic expression.
\(E=\log_{81}3.\)
We will be using the following logarithmic properties:
\((i)~\log_ba=\dfrac{\log a}{\log b},\\\\(ii)~\log a^b=b\log a.\)
The solution is as follows:
\(E\\\\=\log_{81}3\\\\\\=\dfrac{\log 3}{\log 81}\\\\\\=\dfrac{\log 3}{\log 3^4}\\\\\\=\dfrac{\log 3}{4\log 3}\\\\\\=\dfrac{1}{4}.\)
Thus, the required value of the given expression is \(\dfrac{1}{4}.\)
