Answer
$x=\pm1$
Work Step by Step
$6^{x^{2}-1}=6^{1-x^{2}}$
Simply use the one-to-one property to solve this equation. Make the exponents on each side of the equation equal:
$x^{2}-1=1-x^{2}$
Take the $-x^{2}$ to the left side of the equation and the $-1$ to the right side:
$x^{2}+x^{2}=1+1$
Simplify both sides:
$2x^{2}=2$
Take the $2$ to divide the right side:
$x^{2}=\dfrac{2}{2}$
$x^{2}=1$
Take the square root of both sides of the equation:
$\sqrt{x^{2}}=\sqrt{1}$
$x=\pm1$
