Reduce[Exists[{x, y, z}, {x > 0, y > 0, z > 0,
2 + Log[2, x] == 3 + Log[3, y] == 5 + Log[5, z], #}],
Reals] & /@ {x > y > z, x > z > y, y > x > z, y > z > x}
Since the solutions to logarithmic equations are not unique, it's impossible to determine a single exact solution for the equation. The method mentioned above cannot verify the correctness of the third option (Option C). Are there alternative approaches that can perfectly resolve this issue?
