3^p*3^p=1/9

Solution for 3^p*3^p=1/9 equation:

3^p*3^p=1/9

We move all terms to the left:

3^p*3^p-(1/9)=0

We add all the numbers together, and all the variables

3^p*3^p-(+1/9)=0

Wy multiply elements

9p^2-(+1/9)=0

We get rid of parentheses

9p^2-1/9=0

We multiply all the terms by the denominator


9p^2*9-1=0

Wy multiply elements

81p^2-1=0

a = 81; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·81·(-1)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18}{2*81}=\frac{-18}{162}
=-1/9
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18}{2*81}=\frac{18}{162}
=1/9
$