Solving a logarithmic equation with variables on each side. Okay, so while doing a problem for my calculus class I was required to graph two functions in order to see where they intersect, as according to my teacher there is no way to solve it analytically. This really bothers me and there must be a way to solve it. I did research online to try to solve it, but I had no idea where to even start. Here is the equation. y = ln(5 - y)

gasavasiv 2022-10-24 Answered
Solving a logarithmic equation with variables on each side
Okay, so while doing a problem for my calculus class I was required to graph two functions in order to see where they intersect, as according to my teacher there is no way to solve it analytically.
This really bothers me and there must be a way to solve it. I did research online to try to solve it, but I had no idea where to even start.
Here is the equation.
y = ln ( 5 y )
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Answers (1)

fjaldangi
Answered 2022-10-25 Author has 9 answers
For this one you need Lambert's Omega function which is defined as:
W ( z ) e W ( z ) = z
Your equation can be written as:
x = ln ( 5 x )
x = ln ( 5 x )
e x + x = 5
Which solution is x = 5 W ( e 5 )
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