Solve the exponential equation by taking the logarithm of both sides. $11 - 4 ^ { x ^ { 2 } } = 3$
A) $\left\{ \frac { \sqrt { \ln x } } { 4 } \right\}$
B) $\left\{ - \frac { \sqrt { 6 } } { 2 } , \frac { \sqrt { 6 } } { 2 } \right\}$
C) $\{ - \sqrt { \ln x } , \sqrt { \ln x } \}$
D) $\{ \sqrt { 2 } , - \sqrt { 2 } \}$

Question

Quizplus · Accepted Answer

First, isolate the exponential expression: $11 - 4^{x^2} = 3$ becomes $4^{x^2} = 8$. Taking the logarithm of both sides with base 4, we get $x^2 = \log_4 8$. Since $8 = 4^{3/2}$, it follows that $x^2 = 3/2$, and thus $x = \pm \sqrt{3/2}$, which simplifies to $x = \pm \sqrt{6}/2$.

Solve the Exponential Equation by Taking the Logarithm of Both 11−4x2=311 - 4 ^ { x ^ { 2 } } = 311−4x2=3

Solve the Exponential Equation by Taking the Logarithm of Both $11 - 4 ^ { x ^ { 2 } } = 3$