Answer
$x=\pm2$
Work Step by Step
$10^{2x^{2}-3}=10^{9-x^{2}}$
Simply use the one-to-one property to solve this equation. Make the exponents on both sides of the equation equal:
$2x^{2}-3=9-x^{2}$
Take the $-x^{2}$ to the left side of the equation and take $-3$ to the right side:
$2x^{2}+x^{2}=9+3$
Simplify both sides:
$3x^{2}=12$
Take the $3$ to divide the right side:
$x^{2}=\dfrac{12}{3}$
$x^{2}=4$
Take the square root of both sides of the equation:
$\sqrt{x^{2}}=\sqrt{4}$
$x=\pm2$