9^x=4/9*4^x

Solution for 9^x=4/9*4^x equation:

9^x=4/9*4^x

We move all terms to the left:

9^x-(4/9*4^x)=0


Domain of the equation: 9*4^x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

9^x-4/9*4^x=0

We multiply all the terms by the denominator


9^x*9*4^x-4=0

Wy multiply elements

324x^2*4-4=0

Wy multiply elements

1296x^2-4=0

a = 1296; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·1296·(-4)
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-144}{2*1296}=\frac{-144}{2592}
=-1/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+144}{2*1296}=\frac{144}{2592}
=1/18
$