9^x=1/3(27^x)

Solution for 9^x=1/3(27^x) equation:

9^x=1/3(27^x)

We move all terms to the left:

9^x-(1/3(27^x))=0


Domain of the equation: 327^x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

9^x-1/327^x=0

We multiply all the terms by the denominator


9^x*327^x-1=0

Wy multiply elements

2943x^2-1=0

a = 2943; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·2943·(-1)
Δ = 11772
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{11772}=\sqrt{36*327}=\sqrt{36}*\sqrt{327}=6\sqrt{327}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{327}}{2*2943}=\frac{0-6\sqrt{327}}{5886}
=-\frac{6\sqrt{327}}{5886}
=-\frac{\sqrt{327}}{981}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{327}}{2*2943}=\frac{0+6\sqrt{327}}{5886}
=\frac{6\sqrt{327}}{5886}
=\frac{\sqrt{327}}{981}
$