3^x=9/27^x

Solution for 3^x=9/27^x equation:

3^x=9/27^x

We move all terms to the left:

3^x-(9/27^x)=0


Domain of the equation: 27^x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

3^x-9/27^x=0

We multiply all the terms by the denominator


3^x*27^x-9=0

Wy multiply elements

81x^2-9=0

a = 81; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·81·(-9)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54}{2*81}=\frac{-54}{162}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54}{2*81}=\frac{54}{162}
=1/3
$