Write the expression as a sum and/or difference of ln x and ln y. Assume all variables represent positive real numbers. $\ln \left( \frac { e ^ { 2 } x } { y } \right)$
A) $2 + \ln x - \ln y$
B) $\frac { 2 \ln x } { \ln y }$
C) $\ln e ^ { x } x - \ln y$
D) $\ln e ^ { x } - \ln x - \ln y$

Question

Quizplus · Accepted Answer

The expression $\ln \left( \frac { e ^ { 2 } x } { y } \right)$ simplifies to $2 + \ln x - \ln y$ by using properties of logarithms. The term $e^2$ simplifies to 2 when taken as a coefficient in front of the logarithm because $\ln(e^2) = 2$, and the division inside the logarithm translates to subtraction outside the logarithm.

Write the Expression as a Sum And/or Difference of Ln ln⁡(e2xy)\ln \left( \frac { e ^ { 2 } x } { y } \right)ln(ye2x​)

Write the Expression as a Sum And/or Difference of Ln $\ln \left( \frac { e ^ { 2 } x } { y } \right)$