Modulus And Logarithmic Equations

Modulus and Logarithmic Equations is a focused, exam-oriented module designed to help you master two of the most scoring yet commonly misunderstood topics in Algebra. Whether you are preparing for JEE Main & Advanced, BITSAT, VITEEE, SRMJEEE, WBJEE, MHT-CET, EAMCET, COMEDK, KVPY, NTSE, or Olympiads, this pdf builds the conceptual clarity needed to tackle even the trickiest questions with confidence.

Modulus (absolute value) and logarithms are recurring themes across Algebra, Calculus, Functions, and Inequalities. Questions from these topics appear in almost every engineering and science entrance exam, and often form the foundation for advanced problems in Definite Integration, Limits, and Coordinate Geometry. This module ensures you never lose marks on these high-frequency topics again.

What's Covered

• Understanding Modulus: Definition, geometric meaning on the number line, and properties of |x|

• Modulus Equations & Inequalities: Solving |ax + b| = c, |x − a| + |x − b| = k, and inequalities of the form |x| < a, |x| > a, and their combinations.

• Introduction to Logarithms: Definition, base rules, domain restrictions, and the difference between log and ln

• Logarithmic Properties: Product, quotient, power, change-of-base, and base-switching rules with applications

• Logarithmic Equations: Solving equations of the form logₐ f(x) = b, log f(x) + log g(x) = c, and equations reducible to quadratic form

• Logarithmic Inequalities: Handling base > 1 vs 0 < base < 1 and sign-based reasoning.

Who This Course Is For

• Class 11 & 12 students building their Algebra foundation for board exams and entrance tests.

• JEE Main & Advanced aspirants looking to strengthen high-weightage Algebra topics.

• BITSAT, VITEEE, SRMJEEE, WBJEE, MHT-CET, EAMCET & COMEDK candidates seeking quick, reliable problem-solving methods.

• KVPY, NTSE & Olympiad students aiming to sharpen logical and analytical thinking.

• Droppers and revision-focused learners who want a consolidated, exam-ready revision resource.

By the end of this module, you will be able to solve modulus and logarithmic equations quickly, accurately, and with full conceptual understanding—turning these topics into a reliable source of marks in your entrance exam.