Question 6: Find value of \(x\) in the following:
\((iii)\) \(\quad\) \(\left(\frac{1}{32}\right)^{2x} =64 \)
Solution:
\[
\begin{align*}
\left(\frac{1}{32}\right)^{2x} &=64\\
\left(\frac{1}{2^{5}}\right)^{2x} &=2^{6}\\
\left( 2^{-5}\right)^{2x} &=2^{6}\\
2^{-10x} &=2^{6}\\
\end{align*}
\]
Equating base of \(2\), we have
\[
\begin{align*}
-10x&=6\\
x&=\frac{6}{-10}\\
x&=-\frac{3}{5}
\end{align*}
\]