How to solve 4x−log(x)=0

odcizit49o

odcizit49o

Answered question

2022-11-09

How to solve 4 x log ( x ) = 0
I have a problem solving this equation: 4 x log ( x ) = 0. I can't seem to get this equation to a simpler form featuring logs only or getting rid of the log
Is there a way to solve it without the Lambert-W function?

Answer & Explanation

zastenjkcy

zastenjkcy

Beginner2022-11-10Added 14 answers

Since e 4 x > x for every x R , it is impossible to have e 4 x = x, so that the equation 4 x = log ( x ) has no real solution for x > 0, where this equation is defined.
Nola Aguilar

Nola Aguilar

Beginner2022-11-11Added 4 answers

Applying a bit of algebra, we have
4 x log x = 0
4 x = log x
x = 1 4 log x
Also note that x is greater than log x at every point in ( 0 , ). Multiplying log x is only going to make it smaller. Therefore, there are no real solutions to this equation.

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