Determine the natural numbers $x$, $y$ such that $3 \cdot 2^x+1= 7^y$

Question

Determine the natural numbers $x$, $y$ such that $3\cdot 2^x+1= 7^y$.

I have some not-really-good ideas we can start with:

1. Using the last figure and determine the parity of the number and many more divided.

2. I don't know why I thought of it, but we can use the inequality of environments...it's one of my lasts lessons... Anyways, any idea is welcome and hope one of you can help me! Thank you soo much!