Answer
$\displaystyle \ln\frac{x^{3}y^{2}}{z^{4}}$
Work Step by Step
See Th.5.2.
Property $1$ : $\ln(1)=0$
Property $2$ : $\ln(ab)=\ln a + \ln b$
Property $3$ : $\ln(a^{n})=n\cdot\ln a $
Property 4 : $\displaystyle \ln(\frac{a}{b})=\ln a - \ln b$
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$3\ln x+2\ln y-4\ln z$= ... property $3$...
$\ln x^{3}+\ln y^{2}-\ln z^{4}$= ... property $2$...
$\ln(x^{3}y^{2})-\ln z^{4}$= ... property $4$...
$=\displaystyle \ln\frac{x^{3}y^{2}}{z^{4}}$
