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

gasavasiv

Answered question

2022-10-24

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 )

Answer & Explanation

fjaldangi

fjaldangi

Beginner2022-10-25Added 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 )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?