How to solve an equation like 2^x+x=2?

Ernesto Wagner

Ernesto Wagner

Answered question

2022-11-23

How to solve an equation like 2 x + x = 2?

Answer & Explanation

razbrskaltnV

razbrskaltnV

Beginner2022-11-24Added 6 answers

Notice, you've to use the Product log function:
a x + x = a x = a ln ( a ) W n ( a a ln ( a ) ) ln ( a )
Where: W k ( z ) is the analytic continuation of the product log function and n Z
The real solution is given by (n=1):
a x + x = a x = a ln ( a ) W ( a a ln ( a ) ) ln ( a )
In your example a=2:
2 x + x = 2 x = 2 ln ( 2 ) W ( 4 ln ( 2 ) ) ln ( 2 ) 0.5430004

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