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log4((log2x-3)²)=√7log74 equation

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Numerical solution:

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The solution

You have entered [src] 
   /              2\                
log\(log(2*x) - 3) /     ___        
-------------------- = \/ 7 *log(74)
       log(4)
$$\frac{\log{\left(\left(\log{\left(2 x \right)} - 3\right)^{2} \right)}}{\log{\left(4 \right)}} = \sqrt{7} \log{\left(74 \right)}$$
Simplify
Rapid solution [src] 
               /   ___\
               | \/ 7 |
            log\2     /
      3 - 74           
     e                 
x1 = ------------------
             2
$$x_{1} = \frac{1}{2 e^{-3 + 74^{\log{\left(2^{\sqrt{7}} \right)}}}}$$ 
               /   ___\
               | \/ 7 |
            log\2     /
      3 + 74           
     e                 
x2 = ------------------
             2
$$x_{2} = \frac{e^{3 + 74^{\log{\left(2^{\sqrt{7}} \right)}}}}{2}$$ 
x2 = exp(3 + 74^log(2^(sqrt(7))))/2
Sum and product of roots [src] 
sum
          /   ___\             /   ___\
          | \/ 7 |             | \/ 7 |
       log\2     /          log\2     /
 3 - 74               3 + 74           
e                    e                 
------------------ + ------------------
        2                    2
$$\frac{1}{2 e^{-3 + 74^{\log{\left(2^{\sqrt{7}} \right)}}}} + \frac{e^{3 + 74^{\log{\left(2^{\sqrt{7}} \right)}}}}{2}$$ 
=
          /   ___\             /   ___\
          | \/ 7 |             | \/ 7 |
       log\2     /          log\2     /
 3 + 74               3 - 74           
e                    e                 
------------------ + ------------------
        2                    2
$$\frac{1}{2 e^{-3 + 74^{\log{\left(2^{\sqrt{7}} \right)}}}} + \frac{e^{3 + 74^{\log{\left(2^{\sqrt{7}} \right)}}}}{2}$$ 
product
          /   ___\           /   ___\
          | \/ 7 |           | \/ 7 |
       log\2     /        log\2     /
 3 - 74             3 + 74           
e                  e                 
------------------*------------------
        2                  2
$$\frac{1}{2 e^{-3 + 74^{\log{\left(2^{\sqrt{7}} \right)}}}} \frac{e^{3 + 74^{\log{\left(2^{\sqrt{7}} \right)}}}}{2}$$ 
=
 6
e 
--
4
$$\frac{e^{6}}{4}$$ 
exp(6)/4
Numerical answer [src] 
x1 = 3.32118670592301e-1163
x2 = 3.03678194885325e+1164
x2 = 3.03678194885325e+1164
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