Answer: The answer is [tex]\dfrac{2}{3}.[/tex]
Step-by-step explanation: We are given to find the value of [tex]\log_{27}9.[/tex]
Here, we will be using the following properties of logarithm.
[tex](i)~\log a^b=b\log a,\\\\(ii)~\log_ba=\dfrac{\log a}{\log b}.[/tex]
So, we will be solving the given problem using these two as follows.
[tex]\log_{27}9=\dfrac{\log9}{\log27}=\dfrac{\log 3^2}{\log 3^3}=\dfrac{2\log 3}{3\log 3}=\dfrac{2}{3}.[/tex]
Thus, the required value is [tex]\dfrac{2}{3}.[/tex]
