Find all real numbers x that satisfy the given equation. $\left( \frac { 1 } { 81 } \right) ^ { x - 1 } = 3 ^ { 4 - 3 x ^ { 2 } }$
A)0, $- \frac { 4 } { 3 }$
B)0, $\frac { 4 } { 3 }$
C) $- \frac { 4 } { 3 }$
D)0

Question

Quizplus · Accepted Answer

By expressing both sides with base 3, we get $3^{-4(x-1)} = 3^{4-3x^2}$. Equating exponents gives $-4(x-1) = 4-3x^2$, solving which gives $x = 0$ and $x = \frac{4}{3}$.

Find All Real Numbers X That Satisfy the Given Equation (181)x−1=34−3x2\left( \frac { 1 } { 81 } \right) ^ { x - 1 } = 3 ^ { 4 - 3 x ^ { 2 } }(811​)x−1=34−3x2

Find All Real Numbers X That Satisfy the Given Equation $\left( \frac { 1 } { 81 } \right) ^ { x - 1 } = 3 ^ { 4 - 3 x ^ { 2 } }$