What is the pure strategy nash equilibrium of the game

Question

Problem: A husband and wife live together in a beautiful little house. Both enjoy having a clean and beautiful house, which is the result of both of their cleaning efforts, but both the husband and the wife dislike putting any actually effort into cleaning. Also, they both value the cleanliness of the house differently.

They each choose a non-negative number, e^H, e^W representing  how much effort to devote to cleaning, and each has the utility function

u^W(e^H, e^W) = ln (e^H + e^W) - e^W

u^H(e^H, e^W) = kln(e^H + e^W) - e^H

k < 1

Q1. What is the pure strategy Nash equilibrium of this game?

Q2. How does the distribution of effort in the equilibrium reflect each player’s taste for cleanliness?  Does this seem fair to you?