(102/100)2n=2

Solution for (102/100)2n=2 equation:

(102/100)2n=2

We move all terms to the left:

(102/100)2n-(2)=0


Domain of the equation: 100)2n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+102/100)2n-2=0

We multiply parentheses

204n^2-2=0

a = 204; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·204·(-2)
Δ = 1632
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{102}}{2*204}=\frac{0-4\sqrt{102}}{408}
=-\frac{4\sqrt{102}}{408}
=-\frac{\sqrt{102}}{102}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{102}}{2*204}=\frac{0+4\sqrt{102}}{408}
=\frac{4\sqrt{102}}{408}
=\frac{\sqrt{102}}{102}
$