(4/11)n=8/11

Solution for (4/11)n=8/11 equation:

(4/11)n=8/11

We move all terms to the left:

(4/11)n-(8/11)=0


Domain of the equation: 11)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+4/11)n-(+8/11)=0

We multiply parentheses

4n^2-(+8/11)=0

We get rid of parentheses

4n^2-8/11=0

We multiply all the terms by the denominator


4n^2*11-8=0

Wy multiply elements

44n^2-8=0

a = 44; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·44·(-8)
Δ = 1408
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:

$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{22}}{2*44}=\frac{0-8\sqrt{22}}{88}
=-\frac{8\sqrt{22}}{88}
=-\frac{\sqrt{22}}{11}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{22}}{2*44}=\frac{0+8\sqrt{22}}{88}
=\frac{8\sqrt{22}}{88}
=\frac{\sqrt{22}}{11}
$