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log^(2)(2x-1)=3 equation

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Numerical solution:

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The solution

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   2             
log (2*x - 1) = 3
log⁡(2x−1)2=3\log{\left(2 x - 1 \right)}^{2} = 3
Simplify
The graph
05-10-51015050
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
       ___           ___
     \/ 3         -\/ 3 
1   e        1   e      
- + ------ + - + -------
2     2      2      2
(12e3+12)+(12+e32)\left(\frac{1}{2 e^{\sqrt{3}}} + \frac{1}{2}\right) + \left(\frac{1}{2} + \frac{e^{\sqrt{3}}}{2}\right) 
=
       ___       ___
     \/ 3     -\/ 3 
    e        e      
1 + ------ + -------
      2         2
12e3+1+e32\frac{1}{2 e^{\sqrt{3}}} + 1 + \frac{e^{\sqrt{3}}}{2} 
product
/       ___\ /        ___\
|     \/ 3 | |     -\/ 3 |
|1   e     | |1   e      |
|- + ------|*|- + -------|
\2     2   / \2      2   /
(12+e32)(12e3+12)\left(\frac{1}{2} + \frac{e^{\sqrt{3}}}{2}\right) \left(\frac{1}{2 e^{\sqrt{3}}} + \frac{1}{2}\right) 
=
     /  ___\
    2|\/ 3 |
cosh |-----|
     \  2  /
cosh⁡2(32)\cosh^{2}{\left(\frac{\sqrt{3}}{2} \right)} 
cosh(sqrt(3)/2)^2
Rapid solution [src] 
            ___
          \/ 3 
     1   e     
x1 = - + ------
     2     2
x1=12+e32x_{1} = \frac{1}{2} + \frac{e^{\sqrt{3}}}{2} 
             ___
          -\/ 3 
     1   e      
x2 = - + -------
     2      2
x2=12e3+12x_{2} = \frac{1}{2 e^{\sqrt{3}}} + \frac{1}{2} 
x2 = exp(-sqrt(3))/2 + 1/2
Numerical answer [src] 
x1 = 3.32611683701705
x2 = 0.588460603158882
x2 = 0.588460603158882
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