A note on ternary purely exponential diophantine equations

Let $a,b,c$ be fixed coprime positive integers with min,b,c\>1, and let m=max ,b,c\. Using the Gel'fond--Baker method, we prove that all positive integer solutions $(x,y,z)$ of the equation aˣ+bʸ=cᶻ satisfy $max \{x,y,z\}<155000(log m