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


Answer:

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

Step by Step Explanation:
  1. According to the change of base formula of logarithm, ^@log _b m = \dfrac{ log _a m }{ log _a b } ^@
  2. ^@\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 }^@.

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