(1/9)2n=27n

Solution for (1/9)2n=27n equation:

(1/9)2n=27n

We move all terms to the left:

(1/9)2n-(27n)=0


Domain of the equation: 9)2n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+1/9)2n-27n=0

We add all the numbers together, and all the variables

-27n+(+1/9)2n=0

We multiply parentheses

2n^2-27n=0

a = 2; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·2·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*2}=\frac{0}{4}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*2}=\frac{54}{4}
=13+1/2
$