# Solving for a in an equation with factorials and exponents

Published on October 23, 2024

The solution to the equation 3^(a^2 - 10a + 25)! = 729^4 is a = 3 or a = 7, found by equating exponents after expressing both sides with the same base and solving the resulting quadratic equation.

## Question

If \[ 3^{\left(a^{2}-10 a+25\right)!}=729^{4} \] Then, \[ a=\text { ? } \]