Mister Exam

lgx=(x-1)*5 equation

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Numerical solution:

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The solution

You have entered [src]
log(x) = (x - 1)*5
$$\log{\left(x \right)} = 5 \left(x - 1\right)$$
The graph
Sum and product of roots [src]
sum
     /    -5\
    W\-5*e  /
1 - ---------
        5    
$$1 - \frac{W\left(- \frac{5}{e^{5}}\right)}{5}$$
=
     /    -5\
    W\-5*e  /
1 - ---------
        5    
$$1 - \frac{W\left(- \frac{5}{e^{5}}\right)}{5}$$
product
  /    -5\ 
-W\-5*e  / 
-----------
     5     
$$- \frac{W\left(- \frac{5}{e^{5}}\right)}{5}$$
=
  /    -5\ 
-W\-5*e  / 
-----------
     5     
$$- \frac{W\left(- \frac{5}{e^{5}}\right)}{5}$$
-LambertW(-5*exp(-5))/5
Rapid solution [src]
x1 = 1
$$x_{1} = 1$$
       /    -5\ 
     -W\-5*e  / 
x2 = -----------
          5     
$$x_{2} = - \frac{W\left(- \frac{5}{e^{5}}\right)}{5}$$
x2 = -LambertW(-5*exp(-5))/5
Numerical answer [src]
x1 = 1.0
x2 = 0.00697715365114474
x2 = 0.00697715365114474