Question

solve for $a$
$3^{2a-1} = 3^{2}$

Explanation:

Step1: Set exponents equal

Since the bases are equal ($3=3$), we can equate the exponents directly.
$2a - 1 = 2$

Step2: Isolate the term with $a$

Add 1 to both sides of the equation to isolate the term containing $a$.
$2a = 2 + 1$
$2a = 3$

Step3: Solve for $a$

Divide both sides by 2 to solve for $a$.
$a = \frac{3}{2}$

Answer:

$a = \frac{3}{2}$