
\begin{enumerate}
\item $\begin{aligned}[t]
\ln(8)-\ln(2) & = \ln\big(2^3\big)-\ln(2)\\
              & = 3\ln(2)-\ln(2)\\
              & = (3-1)\ln(2)\\
              & = \boxed{2\ln(2)}
\end{aligned}$

\item $\begin{aligned}[t]
3\ln(4)-\ln(256) & = 3\ln\big(2^2\big) - \ln\big(2^8\big)\\
                 & = 3\times2\ln(2)-8\ln(2)\\
                 & = (6-8)\ln(2)\\
                 & = \boxed{-2\ln(2)}
\end{aligned}$

\item $\begin{aligned}[t]
2\ln(2)-\ln(16)+\ln(128) & = 2\ln(2) - \ln\big(2^4\big) + \ln\big(2^7\big)\\
					     & = 2\ln(2) - 4\ln(2) + 7\ln(2)\\
					     & = (2-4+7)\ln(2)\\
					     & = \boxed{ 5\ln(2) }
\end{aligned}$

\item $\begin{aligned}[t]
\ln(27) - 8\ln(9) + 14\ln(3) & = \ln\big(3^3\big) - 8\ln\big(3^2\big) + 14\ln(3)\\
							 & = 3\ln(3) - 8\times2\ln(3) + 14\ln(3)\\
							 & = (3-16+14)\ln(3)\\
							 & = \boxed{ \ln(3) }
\end{aligned}$

\item $\begin{aligned}[t]
\ln(125) - 5\ln(5) + 4\ln(25) & = \ln\big(5^3\big) - 5\ln(5) + 4\ln\big(5^2\big)\\
							  & = 3\ln(5)-5\ln(5) + 8\ln(5)\\
							  & = (3-5+8)\ln(5)\\
							  & = \boxed{6\ln(5)}
\end{aligned}$

\item $\begin{aligned}[t]
7\ln(7)-9\ln(49)+\ln(343) & = 7\ln(7) - 9\ln\big(7^2\big) + \ln\big(7^3\big)\\
						  & = 7\ln(7) - 18\ln(7) + 3\ln(7)\\
						  & = (7-18+3)\ln(7)\\
						  & = \boxed{ -8\ln(7) }
\end{aligned}$
\end{enumerate}
