3^n*9^n=27

Solution for 3^n*9^n=27 equation:

3^n*9^n=27

We move all terms to the left:

3^n*9^n-(27)=0

Wy multiply elements

27n^2-27=0

a = 27; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·27·(-27)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54}{2*27}=\frac{-54}{54}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54}{2*27}=\frac{54}{54}
=1
$