Answer
$\frac{11}{6}$
Work Step by Step
div $\textbf{F}=\nabla\cdot \textbf{F}=\nabla\cdot\langle\ln(xyz),\ln(xyz),\ln(xyz)\rangle$
$=\frac{\partial}{\partial x}(\ln(xyz))+\frac{\partial}{\partial y}(\ln(xyz))+\frac{\partial}{\partial z}(\ln(xyz))$
$=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$
Knowing that $(x,y,z)=(3,2,1)$, We get
div $\textbf{F}=\frac{1}{3}+\frac{1}{2}+\frac{1}{1}=\frac{11}{6}$
