Question

solve the equation.
$9^{3x - 3} = 81^{x + 3}$
the solution set is {\box}.

Explanation:

Step1: Rewrite bases as powers of 3

$9^{3x-3}=(3^2)^{3x-3}$, $81^{x+3}=(3^4)^{x+3}$

Step2: Simplify exponents using power rule

$(3^2)^{3x-3}=3^{2(3x-3)}=3^{6x-6}$; $(3^4)^{x+3}=3^{4(x+3)}=3^{4x+12}$

Step3: Set exponents equal (same base)

$6x - 6 = 4x + 12$

Step4: Solve for x, isolate variables

$6x - 4x = 12 + 6$
$2x = 18$

Step5: Solve for x, divide by 2

$x=\frac{18}{2}=9$

Answer:

$\{9\}$