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logx3√(7*10√(7))=-1 equation

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Numerical solution:

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The solution

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            __________     
           /      ___      
log(x)*3*\/  70*\/ 7   = -1
3log⁡(x)707=−13 \log{\left(x \right)} \sqrt{70 \sqrt{7}} = -1
Simplify
Detail solution
Given the equation
3log⁡(x)707=−13 \log{\left(x \right)} \sqrt{70 \sqrt{7}} = -1
310⋅734log⁡(x)=−13 \sqrt{10} \cdot 7^{\frac{3}{4}} \log{\left(x \right)} = -1
Let's divide both parts of the equation by the multiplier of log =3*7^(3/4)*sqrt(10)
log⁡(x)=−1074210\log{\left(x \right)} = - \frac{\sqrt{10} \sqrt[4]{7}}{210}
This equation is of the form:
log(v)=p

By definition log
v=e^p

then
x=e−1310⋅734x = e^{- \frac{1}{3 \sqrt{10} \cdot 7^{\frac{3}{4}}}}
simplify
x=e−1074210x = e^{- \frac{\sqrt{10} \sqrt[4]{7}}{210}}
The graph
-12.5-10.0-7.5-5.0-2.50.02.55.07.510.012.515.0-500500
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
       4 ___   ____ 
      -\/ 7 *\/ 10  
      --------------
           210      
x1 = e
x1=e−1074210x_{1} = e^{- \frac{\sqrt{10} \sqrt[4]{7}}{210}} 
x1 = exp(-sqrt(10)*7^(1/4)/210)
Sum and product of roots [src] 
sum
  4 ___   ____ 
 -\/ 7 *\/ 10  
 --------------
      210      
e
e−1074210e^{- \frac{\sqrt{10} \sqrt[4]{7}}{210}} 
=
  4 ___   ____ 
 -\/ 7 *\/ 10  
 --------------
      210      
e
e−1074210e^{- \frac{\sqrt{10} \sqrt[4]{7}}{210}} 
product
  4 ___   ____ 
 -\/ 7 *\/ 10  
 --------------
      210      
e
e−1074210e^{- \frac{\sqrt{10} \sqrt[4]{7}}{210}} 
=
  4 ___   ____ 
 -\/ 7 *\/ 10  
 --------------
      210      
e
e−1074210e^{- \frac{\sqrt{10} \sqrt[4]{7}}{210}} 
exp(-7^(1/4)*sqrt(10)/210)
Numerical answer [src] 
x1 = 0.975803791280659
x1 = 0.975803791280659
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