Expand the logarithmic expression. $\ln \left( X Y ^ { 2 } Z ^ { 3 } \right)$
A) $\frac { \ln X + 2 \ln Y } { 3 \ln Z }$
B) $\frac { 2 \ln X + \ln Y ^ { 2 } } { 3 Z }$
C) $\ln ( \mathrm { X } + 2 \mathrm { Y } + 3 \mathrm { Z } )$
D) $\ln X + 2 \ln Y + 3 \ln Z$
E) $6 \ln ( X + Y + Z )$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we have:
$$\ln \left( X Y ^ { 2 } Z ^ { 3 } \right) = \ln X + \ln Y^2 + \ln Z^3 = \ln X + 2\ln Y + 3\ln Z$$ Option D is the only one that matches this result.

Expand the Logarithmic Expression ln⁡(XY2Z3)\ln \left( X Y ^ { 2 } Z ^ { 3 } \right)ln(XY2Z3)

Expand the Logarithmic Expression $\ln \left( X Y ^ { 2 } Z ^ { 3 } \right)$