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log(2)(x²-1)=log(2)(2x-1) equation

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Numerical solution:

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The solution

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log(2)*\x  - 1/ = log(2)*(2*x - 1)
(x2−1)log⁡(2)=(2x−1)log⁡(2)\left(x^{2} - 1\right) \log{\left(2 \right)} = \left(2 x - 1\right) \log{\left(2 \right)}
Simplify
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
(x2−1)log⁡(2)=(2x−1)log⁡(2)\left(x^{2} - 1\right) \log{\left(2 \right)} = \left(2 x - 1\right) \log{\left(2 \right)}
to
−(2x−1)log⁡(2)+(x2−1)log⁡(2)=0- \left(2 x - 1\right) \log{\left(2 \right)} + \left(x^{2} - 1\right) \log{\left(2 \right)} = 0
Expand the expression in the equation
−(2x−1)log⁡(2)+(x2−1)log⁡(2)=0- \left(2 x - 1\right) \log{\left(2 \right)} + \left(x^{2} - 1\right) \log{\left(2 \right)} = 0
We get the quadratic equation
x2log⁡(2)−2xlog⁡(2)=0x^{2} \log{\left(2 \right)} - 2 x \log{\left(2 \right)} = 0
This equation is of the form
a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=log⁡(2)a = \log{\left(2 \right)}
b=−2log⁡(2)b = - 2 \log{\left(2 \right)}
c=0c = 0
, then
D = b^2 - 4 * a * c = 

(-2*log(2))^2 - 4 * (log(2)) * (0) = 4*log(2)^2

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
x1=2x_{1} = 2
x2=0x_{2} = 0
The graph
02468-8-6-4-21210-10200-100
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 0
x1=0x_{1} = 0 
x2 = 2
x2=2x_{2} = 2 
x2 = 2
Sum and product of roots [src] 
sum
2
22 
=
2
22 
product
0*2
0⋅20 \cdot 2 
=
0
00 
0
Numerical answer [src] 
x1 = 2.0
x2 = 0.0
x2 = 0.0
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