solve the equation 3^2x=6561

Answer 1

Starting with $3^{2x} = 6561$, we can write $6561$ as a power of $3$: $6561 = 3^8$. Therefore, we have $3^{2x} = 3^8$, which implies that $2x = 8$. Solving for $x$, we find $x = \boxed{4}$.