Answer
$$ \frac{d y}{d t}=\frac{1}{t}\\ $$
Work Step by Step
Given $$ y = \log _{2}\left(8 t^{\ln 2}\right)\\$$
Since $$\log_{a}z=\frac{\ln z}{\ln a}$$ So, we have
\begin{aligned}
y& =\log _{2}\left(8 t^{\ln 2}\right)\\
&=\frac{\ln \left(8\ t^{\ln 2} \right)}{\ln 2}\\
&=\frac{\ln 8+\ln \left(t^{\ln 2} \right)}{\ln 2}\\
&=\frac{\ln 2^3+\ln \left(t^{\ln 2} \right)}{\ln 2}\\
&=\frac{3 \ln 2+(\ln 2)(\ln t)}{\ln 2}\\
&=3+\ln t \\
&\Rightarrow \frac{d y}{d t}=\frac{1}{t}\\
\end{aligned}
