“方程解的讨论”是高中数学中一类难度较高的问题,是高考的热门话题。这类问题综合性大,包含了诸如:解指、对数不等式,换元法,函数思想,数形结合思想等不等式,函数方程中的重要知识点和方法。因此,这类问题在培养学生思维的逻辑性、严密性、灵活性以及思维的深度和广度上,有着其他问题不可替代的作用。本文就解决这类问题的四种典型方法:方程法、根的分布法、分离字母法、函数法,从分析、解决问题的角度,讨论了解题的步骤和需要注重的问题并比较了各种方法的特点,应用范围,指出了它们的局限性,突出了方法的实质。例题:设 a∈R,讨论关于 x 的方程 lg(x-1)+lg “Discussion of the equation solution” is a high difficulty problem in high school mathematics, and it is a hot topic in college entrance examination. This kind of problem is comprehensive and contains many important inequalities such as: solution, logarithmic inequality, substitution method, function idea, number-form combination idea, and important knowledge points and methods in function equations. Therefore, such problems have irreplaceable roles in cultivating students’ logic, rigor, flexibility, and depth and breadth of thinking. In this paper, four typical methods for solving such problems are: equation method, root distribution method, separated alphabetic method, and function method. From the perspective of analysis and problem solving, the steps for understanding the problem and the problems to be emphasized are discussed and compared. The features of these methods and their scope of application point out their limitations and highlight the essence of the method. Example: Let a∈R discuss the equation for x lg(x-1)+lg