Solve the logarithmic equation. $\ln y ^ { 2 } = 10$
A) $\{ \ln 2 , - \ln 2 \}$
B) $\left\{ \frac { e } { 5 } \right\}$
C) $\left\{ e ^ { 5 } , - e ^ { 5 } \right\}$
D) $\left\{ \frac { \sqrt { 10 } } { \ln } , - \frac { \sqrt { 10 } } { \ln } \right\}$

Question

Quizplus · Accepted Answer

First, rewrite the equation as $2 \ln y = 10$, which simplifies to $\ln y = 5$. Exponentiating both sides with base $e$ gives $y = e^5$. However, since the original equation involves $y^2$, both $y = e^5$ and $y = -e^5$ are solutions, because squaring either value will satisfy the original equation.

Solve the Logarithmic Equation ln⁡y2=10\ln y ^ { 2 } = 10lny2=10

Solve the Logarithmic Equation $\ln y ^ { 2 } = 10$