3^2n=1/27

Solution for 3^2n=1/27 equation:

3^2n=1/27

We move all terms to the left:

3^2n-(1/27)=0

We add all the numbers together, and all the variables

3^2n-(+1/27)=0

We get rid of parentheses

3^2n-1/27=0

We multiply all the terms by the denominator


3^2n*27-1=0

Wy multiply elements

81n^2-1=0

a = 81; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·81·(-1)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18}{2*81}=\frac{-18}{162}
=-1/9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18}{2*81}=\frac{18}{162}
=1/9
$