Question 6: Find value of \(x\) in the following:
\((ii)\) \(\quad\) \(\left(\frac{1}{9}\right)^{3x} =27 \)
Solution:
\[
\begin{align*}
\left(\frac{1}{9}\right)^{3x} &=27\\
\left(\frac{1}{3^{2}}\right)^{3x} &=3^{3}\\
( 3)^{-2\times 3x} &=3^{3}\\
3^{-6x} &=3^{3}\\
\end{align*}
\]
Equating base of \(3\), we have
\[
\begin{align*}
-6x&=3\\
x&=\frac{3}{-6}\\
x&=-\frac{1}{2}
\end{align*}
\]