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log(x)=x-5

log(x)=x-5 equation

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Numerical solution:

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The solution

You have entered [src] 
log(x) = x - 5
log⁡(x)=x−5\log{\left(x \right)} = x - 5
Simplify
The graph
-7.5-5.0-2.50.02.55.07.510.012.515.0-2525
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
       /  -5\
x1 = -W\-e  /
x1=−W(−1e5)x_{1} = - W\left(- \frac{1}{e^{5}}\right) 
       /  -5    \
x2 = -W\-e  , -1/
x2=−W−1(−1e5)x_{2} = - W_{-1}\left(- \frac{1}{e^{5}}\right) 
x2 = -LambertW(-exp(-5, -1))
Sum and product of roots [src] 
sum
   /  -5\    /  -5    \
- W\-e  / - W\-e  , -1/
−W(−1e5)−W−1(−1e5)- W\left(- \frac{1}{e^{5}}\right) - W_{-1}\left(- \frac{1}{e^{5}}\right) 
=
   /  -5\    /  -5    \
- W\-e  / - W\-e  , -1/
−W(−1e5)−W−1(−1e5)- W\left(- \frac{1}{e^{5}}\right) - W_{-1}\left(- \frac{1}{e^{5}}\right) 
product
  /  -5\ /  /  -5    \\
-W\-e  /*\-W\-e  , -1//
−W(−1e5)(−W−1(−1e5))- W\left(- \frac{1}{e^{5}}\right) \left(- W_{-1}\left(- \frac{1}{e^{5}}\right)\right) 
=
 /  -5\  /  -5    \
W\-e  /*W\-e  , -1/
W(−1e5)W−1(−1e5)W\left(- \frac{1}{e^{5}}\right) W_{-1}\left(- \frac{1}{e^{5}}\right) 
LambertW(-exp(-5))*LambertW(-exp(-5), -1)
Numerical answer [src] 
x1 = 0.00678381135209697
x2 = 6.93684740722022
x2 = 6.93684740722022
The graph
log(x)=x-5 equation
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