Solve $\ln x ^ { 2 } = 3$ for $x$.
A) $e ^ { 9 }$
B) $10 ^ { \sqrt { 3 } }$
C) $e ^ { \sqrt { 3 } }$
D) $- e ^ { 3 / 2 } , e ^ { 3 / 2 }$
E) no solution

Question

Quizplus · Accepted Answer

The equation $\ln x^2 = 3$ can be rewritten as $2\ln x = 3$, which simplifies to $\ln x = \frac{3}{2}$. This means $x = e^{3/2}$. However, since $x^2$ was inside the logarithm, both positive and negative roots are valid, leading to solutions $x = e^{3/2}$ and $x = -e^{3/2}$.

Solve ln⁡x2=3\ln x ^ { 2 } = 3lnx2=3 For xxx A)

Solve $\ln x ^ { 2 } = 3$ For $x$
A)