### Find the value of ^@log _{ 81 } 243^@.

**Answer:**

^@\dfrac { 5 } { 4 }^@

**Step by Step Explanation:**

- According to the change of base formula of logarithm, ^@log _b m = \dfrac{ log _a m }{ log _a b } ^@
- ^@\begin{align} & log _{ 81 } 243 = \dfrac{ log _3 243 } { log _3 81} \\
\implies & log _{ 81 } 243 = \dfrac { log _3 3^5 }{ log _3 3^4 } \\
\implies & log _{ 81 } 243 = \dfrac { 5 log _3 3} { 4 log _3 3 } \\
\implies & log _{ 81 } 243 = \dfrac { 5 } { 4 }
\end{align}^@

Hence, the value of ^@log _{ 81 } 243^@ is ^@\dfrac { 5 } { 4 }^@.