Mastering Absolute Values, Logarithms, and Complex Inequalities

Higher-level mathematics and computational science rely heavily on a strong command of algebraic identities, inequalities, and functions like logarithms and absolute values. This course provides the rigorous foundation you need to succeed. By the end of this course, you will be able to confidently manipulate complex algebraic expressions, determine the domain and range of sophisticated functions, and solve polynomial and rational inequalities using systematic analytical methods. What you'll learn: * Understand fundamental algebraic identities and their application in simplifying complex expressions. * Master the properties of logarithms and exponential functions, including change-of-base formulas. * Analyze equations and inequalities involving absolute values (modulus) and piecewise functions. * Apply the sign chart method (Wavy Curve technique) to accurately solve polynomial and rational inequalities. * Practice defining the valid domain and range for various combined functions involving logs and absolute values. The material begins with a review of essential algebraic rules and gradually progresses through specialized topics like logarithmic properties and the analytical methods used for solving complex inequalities. You will apply these concepts through carefully structured practice exercises. This course is designed for absolute beginners or students needing a rigorous review of foundational math before starting advanced high school or university-level courses. No prior specialized mathematical knowledge is required. Start building your essential mathematical toolkit today.