(1/4)^x=256x=

Solution for (1/4)^x=256x= equation:

(1/4)^x=256x=

We move all terms to the left:

(1/4)^x-(256x)=0


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)^x-256x=0

We add all the numbers together, and all the variables

-256x+(+1/4)^x=0

We multiply all the terms by the denominator


-256x*4)^x+(+1=0

Wy multiply elements

-1024x^2+1=0

a = -1024; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-1024)·1
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64}{2*-1024}=\frac{-64}{-2048}
=1/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64}{2*-1024}=\frac{64}{-2048}
=-1/32
$