Solve $\ln x ^ { 2 } = 13$ for $x$.
A) $e ^ { 169 }$
B) $10 ^ { \sqrt { 3 } }$
C) $e ^ { \sqrt { 13 } }$
D) $- e ^ { 13 / 2 } , e ^ { 13 / 2 }$
E) no solution

Question

Quizplus · Accepted Answer

To solve the equation $\ln x^2 = 13$, we first use the property of logarithms that allows us to bring the exponent in front: $2\ln x = 13$. Dividing both sides by 2 gives $\ln x = \frac{13}{2}$. To solve for $x$, we exponentiate both sides with base $e$, resulting in $x = e^{13/2}$. However, since $x^2$ was inside the logarithm, there are two solutions: $x = e^{13/2}$ and $x = -e^{13/2}$, because squaring either positive or negative $e^{13/2}$ gives the same result inside the logarithm.

Solve ln⁡x2=13\ln x ^ { 2 } = 13lnx2=13 For xxx A)

Solve $\ln x ^ { 2 } = 13$ For $x$
A)