A Pillai-Catalan-type problem involving Fibonacci numbers

This paper addresses A Pillai-Catalan-type problem assosiated with Fibonacci numbers. Let $F_n$ be the Fibonacci numbers defined by the recurrence relation $F_1=1$, $F_2=1$ and $F_n=F_{n-1}+F_{n-2}$ for all $n\ge 3$. We will find all positive integer solution to the equation $3^x-F_n{2}^y=1$ using properties of Fibonacci numbers, linear forms of logarithms, and the Baker-Davenport reduction method.