Solve the equation by expressing each side as a power of the same base and then equating exponents.
-$$27 ^ { x } = \frac { 1 } { \sqrt { 3 } }$$
A) $\left\{ - \frac { 1 } { 6 } \right\}$
B) $\left\{ \frac { 1 } { 6 } \right\}$
C) $\left\{ - \frac { 1 } { 3 } \right\}$
D) $\{ - 3 \}$

Question

Quizplus · Accepted Answer

First, express both sides of the equation as powers of 3: $27^x = 3^{3x}$ and $\frac{1}{\sqrt{3}} = 3^{-\frac{1}{2}}$. Equating the exponents gives $3x = -\frac{1}{2}$, solving for x gives $x = -\frac{1}{6}$.

Solve the Equation by Expressing Each Side as a Power 27x=1327 ^ { x } = \frac { 1 } { \sqrt { 3 } }27x=3​1​

Solve the Equation by Expressing Each Side as a Power $27 ^ { x } = \frac { 1 } { \sqrt { 3 } }$