Answer
$t=\pm \sqrt{e^3}+1$
Work Step by Step
Recall:
$$\ln{a}=y \longleftrightarrow e^y=a$$
Use the definition above to obtain:
\begin{align*}
\ln{\left(t-1\right)^2}&=3\\\\
e^3&=(t-1)^2\\\\
\pm\sqrt{e^3}&=\sqrt{(t-1)^2}\\\\
\pm\sqrt{e^3}&=t-1\\\\
\pm\sqrt{e^3}+1&=t\\\\
\end{align*}
Check:
\begin{align*}
\ln{\left(\left(\sqrt{e^3}+1-1\right)^2\right)}&\stackrel{?}=3\\\\
\ln{\left(\left(\sqrt{e^3}\right)^2\right)}&\stackrel{?}=3\\\\
\ln{e^3}&\stackrel{?}=3\\\\
3&\stackrel{\checkmark}=3\end{align*}
\begin{align*}
\ln{\left(\left(-\sqrt{e^3}+1-1\right)^2\right)}&\stackrel{?}=3\\\\
\ln{\left(\left(-\sqrt{e^3}\right)^2\right)}&\stackrel{?}=3\\\\
\ln{e^3}&\stackrel{?}=3\\\\
3&\stackrel{\checkmark}=3\end{align*}
