3^-v*3^-3v=243

Solution for 3^-v*3^-3v=243 equation:

3^-v*3^-3v=243

We move all terms to the left:

3^-v*3^-3v-(243)=0

determiningTheFunctionDomain
-v*3^-3v-243+3^=0

We add all the numbers together, and all the variables

-3v-v*3^=0

Wy multiply elements

-3v^2-3v=0

a = -3; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-3)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-3}=\frac{0}{-6}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-3}=\frac{6}{-6}
=-1
$