(3/4)n=81

Solution for (3/4)n=81 equation:

(3/4)n=81

We move all terms to the left:

(3/4)n-(81)=0


Domain of the equation: 4)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+3/4)n-81=0

We multiply parentheses

3n^2-81=0

a = 3; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·3·(-81)
Δ = 972
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:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{3}}{2*3}=\frac{0-18\sqrt{3}}{6}
=-\frac{18\sqrt{3}}{6}
=-3\sqrt{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{3}}{2*3}=\frac{0+18\sqrt{3}}{6}
=\frac{18\sqrt{3}}{6}
=3\sqrt{3}
$