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log5log2x=log7(5+2) equation

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Numerical solution:

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The solution

You have entered [src] 
                  log(7)
log(5*log(2*x)) = ------
                  log(7)
$$\log{\left(5 \log{\left(2 x \right)} \right)} = \frac{\log{\left(7 \right)}}{\log{\left(7 \right)}}$$
Simplify
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
      E
      -
      5
     e 
x1 = --
     2
$$x_{1} = \frac{e^{\frac{e}{5}}}{2}$$ 
x1 = exp(E/5)/2
Sum and product of roots [src] 
sum
 E
 -
 5
e 
--
2
$$\frac{e^{\frac{e}{5}}}{2}$$ 
=
 E
 -
 5
e 
--
2
$$\frac{e^{\frac{e}{5}}}{2}$$ 
product
 E
 -
 5
e 
--
2
$$\frac{e^{\frac{e}{5}}}{2}$$ 
=
 E
 -
 5
e 
--
2
$$\frac{e^{\frac{e}{5}}}{2}$$ 
exp(E/5)/2
Numerical answer [src] 
x1 = 0.861146347726133
x1 = 0.861146347726133
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