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

Starting with the given equation,
\begin{align*}
\ln x^2 &= 3 \
\implies 2 \ln x &= 3  &&	ext{(by logarithmic property of exponents)} \
\implies \ln x &= \frac{3}{2} \
\implies x &= e^{3/2} &&	ext{(by inverse of natural logarithm)} \
\end{align*}
Thus, the answer is D, which includes the only solution, $x=e^{3/2}$, since $\ln x$ is only defined for $x>0$.

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

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