Number of natural solutions of exponential equation

Question

To find number and nature of solutions of equation $$ 2^p + 2^q+ 2^r= 2^s$$ where $p,q,r,s\in\mathbb{N}$ such that $p\ge q\ge r\ge s$.

This is a intermediate part of question at which i m stuck.

Answer 1

Since $p,q,r,s\in\mathbb{N}$, therefore$$p\ge q\ge r\ge s\implies2^p\ge 2^q\ge 2^r\ge 2^s$$Thus, $2^p+2^q+2^r>2^s$, which clearly shows that there are no such $(p,q,r,s)$ that satisfies $$2^p+2^q+2^r=2^s$$