Use the properties of logarithms to expand $\ln \frac { x y ^ { 2 } } { z ^ { 2 } }$ .
A) $\ln x - 2 \ln y - 2 \ln z$
B) $\ln ( x + 2 y - 2 z )$
C) $\frac { \ln x \cdot ( \ln y ) ^ { 2 } } { ( \ln z ) ^ { 2 } }$
D) $\ln x + ( \ln y ) ^ { 2 } - ( \ln z ) ^ { 2 }$
E) $\ln x + 2 \ln y - 2 \ln z$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the expression $\ln \frac { x y ^ { 2 } } { z ^ { 2 } }$ can be expanded as $\ln x + \ln y^2 - \ln z^2$. Applying the power rule of logarithms ($\ln a^b = b \ln a$), this simplifies to $\ln x + 2 \ln y - 2 \ln z$.

Use the Properties of Logarithms to Expand ln⁡xy2z2\ln \frac { x y ^ { 2 } } { z ^ { 2 } }lnz2xy2​

Use the Properties of Logarithms to Expand $\ln \frac { x y ^ { 2 } } { z ^ { 2 } }$