(3/8)n=3/4

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

(3/8)n=3/4

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

3n^2-3/4=0

We multiply all the terms by the denominator


3n^2*4-3=0

Wy multiply elements

12n^2-3=0

a = 12; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·12·(-3)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*12}=\frac{-12}{24}
=-1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*12}=\frac{12}{24}
=1/2
$