Solution

Write the following as a single logarithm

$$\ln 3 + 2 \ln 4$$


$$\begin{array}{rcll} \ln 3 + 2 \ln 4 &=& \ln 3 + \ln 4^2 & \scriptsize{\textrm{using the property of logs: } \log_b x^n = n\log_b x}\\\\ &=& \ln3 + \ln 16\\\\ &=& \ln (3 \cdot 16) & \scriptsize{\textrm{using the property of logs: } \log_b xy = \log_b x + \log_b y}\\\\ &=& \ln 48 \end{array}$$