Question 4: Find the value of \(x\) in the following equations:
\((iii)\) \(\quad\) \(( 81)^{x} =( 243)^{x+2} \)
Solution:
\[
\begin{align*}
( 81)^{x} &=( 243)^{x+2}\\
( 3)^{4x} &=( 3)^{5( x+2)}\\
( 3)^{4x} &=( 3)^{5x+10}\\
\end{align*}
\]
Equating bases, we have
\[
\begin{align*}
4x&=5x+10\\
-10&=5x-4x\\
-5&=x
\end{align*}
\]