(3/8)n=1/4

Solution for (3/8)n=1/4 equation:

(3/8)n=1/4

We move all terms to the left:

(3/8)n-(1/4)=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

(+3/8)n-(+1/4)=0

We multiply parentheses

3n^2-(+1/4)=0

We get rid of parentheses

3n^2-1/4=0

We multiply all the terms by the denominator


3n^2*4-1=0

Wy multiply elements

12n^2-1=0

a = 12; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·12·(-1)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*12}=\frac{0-4\sqrt{3}}{24}
=-\frac{4\sqrt{3}}{24}
=-\frac{\sqrt{3}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*12}=\frac{0+4\sqrt{3}}{24}
=\frac{4\sqrt{3}}{24}
=\frac{\sqrt{3}}{6}
$