Solving for unknown variables on both sides with one unknown an index. I have come across this problem while doing a question out of my textbook.
I am asking about how to solve for $x$ in this equation.
$$50x-22=1.5^{x-1}$$
Thank you.

Equations like this do not lend themselves to algebraic solutions.  You can use various numeric techniques to find $x$.  Alpha finds two solutions, around $0.464, 16.495$  To find them yourself, start by graphing the equation, which will give you good guesses for the solutions.  You can then refine them using bisection, Newton-Raphson, or your favorite method.
