\((vii)\) \(2^x\times 8^x = 64\) then \(x=\)
Option B : \(\frac{3}{2}\)
Explanation:
\[
\begin{align*}
2^x\times 8^x &= 64\\ 2^x\times 2^{3 \times x} &= 64\\ 2^x\times 2^{3x} &= 64\\2^{x+3x} &= 64\\2^{4x} &= 2^6
\end{align*}
\]
Equating exponents on both sides
\[
\begin{align*}
4x &=6\\x &=\frac{6}{4}\\&=\frac{3}{2}\\
\end{align*}
\]