Find the value of ^@log _{ 81 } 243^@. | Math Question and Answer | Edugain Philippines

Login/Register Edugain for School

Philippines

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 $\dfrac { 5 } { 4 }$ .

You can reuse this answer
Creative Commons License