# Solve for x in the equation 3^(x^2)/9^x = 81

Published on October 31, 2024

The equation 3^(x^2)/9^x = 81 is solved by rewriting the equation with the same base, simplifying the denominator, applying the quotient rule for exponents, equating the exponents, rearranging into a quadratic equation, and finally using the quadratic formula to find the two solutions, x = 1 + √5 and x = 1 - √5.

## Question

\( \begin{array}{c}\frac{3^{x^{2}}}{9^{x}}=81 \\ x=?\end{array} \)