solve the equation 3^2x=6561
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 $x = \boxed{4}$.
To solve the equation 3^(2x) = 6561, we can follow these steps:
Step 1: Rewrite 6561 as a power of 3.
Since 3^4 = 81 and 3^5 = 243, we can rewrite 6561 as 3^8.
Step 2: Set the exponents equal to each other.
Since 3^(2x) = 3^8, we can set the exponents equal to each other.
2x = 8
Step 3: Solve for x.
To solve for x, we need to isolate the variable.
Divide both sides of the equation by 2.
x = 8/2
Step 4: Simplify.
x = 4
So, the solution to the equation 3^(2x) = 6561 is x = 4.