How do you solve 3x=3x+5?

1 Answer
Apr 3, 2018

See below.

Explanation:

Making y=3x+5 we have

3y53=y or

3y3353=y

now making 313=eλ we have

eλy353=y or

353=yeλy or

(λ)353=(λy)eλy

At this point we use the Lambert function

https://en.wikipedia.org/wiki/Lambert_W_function

Y=XeXX=W(Y) and then

λy=W((λ)353) or

y=1λW((λ)353)=3x5 and finally

x=5log33W((log39×323))3log3

We have then two solutions

x=1.60981 and x=2.24048

Attached a plot showing the intersections of y=3x and y=3x+5

enter image source here