ysol(x, a, b, alpha, beta, k1) =

Trivial, in some eyes. ;-) This is one of the simpler implicit problems you might write down, since a direct solution exists in the form of the Wright omega function.

syms a y x alpha k1 b beta

ysol(x,a,b,alpha,beta,k1) = solve(a*log(y) - alpha*y + b*log(x) - beta*x - k1,y)

And of course, you have not provided any of the constants. But if you did, I could even evaluate it.

ysol(3,4,5,6,7,8)

double(ysol(1,2,3,4,5,6))

I'd bet for some sets of those parameters, the result will even be real. I don't need to change a lot.

double(ysol(1,-2,3,4,5,6))