256^x=1/x

Solution for 256^x=1/x equation:

256^x=1/x

We move all terms to the left:

256^x-(1/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

256^x-1/x=0

We multiply all the terms by the denominator


256^x*x-1=0

Wy multiply elements

256x^2-1=0

a = 256; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·256·(-1)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32}{2*256}=\frac{-32}{512}
=-1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32}{2*256}=\frac{32}{512}
=1/16
$