(5/8)n=2/5

Solution for (5/8)n=2/5 equation:

(5/8)n=2/5

We move all terms to the left:

(5/8)n-(2/5)=0


Domain of the equation: 8)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+5/8)n-(+2/5)=0

We multiply parentheses

5n^2-(+2/5)=0

We get rid of parentheses

5n^2-2/5=0

We multiply all the terms by the denominator


5n^2*5-2=0

Wy multiply elements

25n^2-2=0

a = 25; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·25·(-2)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{2}}{2*25}=\frac{0-10\sqrt{2}}{50}
=-\frac{10\sqrt{2}}{50}
=-\frac{\sqrt{2}}{5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{2}}{2*25}=\frac{0+10\sqrt{2}}{50}
=\frac{10\sqrt{2}}{50}
=\frac{\sqrt{2}}{5}
$