9^-x=3^-x/3(81)^x

Solution for 9^-x=3^-x/3(81)^x equation:

9^-x=3^-x/3(81)^x

We move all terms to the left:

9^-x-(3^-x/3(81)^x)=0


Domain of the equation: 381^x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1x-(3^-x/381^x)=0

We get rid of parentheses

-1x+x/381^x-3^=0

We multiply all the terms by the denominator


-1x*381^x+x-3^*381^x=0

We add all the numbers together, and all the variables

x-1x*381^x-3^*381^x=0

Wy multiply elements

-381x^2-1143x^2+x=0

We add all the numbers together, and all the variables

-1524x^2+x=0

a = -1524; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-1524)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-1524}=\frac{-2}{-3048}
=1/1524
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-1524}=\frac{0}{-3048}
=0
$