A set is a collection of well-defined objects. These objects may be actually listed or may be specified by a rule. In this article, we shall study the application of the definition of a set. Similarly, we shall study to write sets by roster method and set-builder method. Problems on Definition of a Set: Which […]
In the previous articles, we have studied the basics of set theory and its terminology. In this article, we shall study operations of sets including Union of sets, Intersection of sets, a complement of a set, Cartesian product of sets. The basic operations on sets are: Union of sets Intersection of sets A complement of […]
A set is a collection of well-defined objects. These objects may be actually listed or may be specified by a rule. Sets are denoted by a capital letter like A, B, C…. and an object belonging to them (element of the set) are denoted by a small case letter like a, b, c,… of the […]
Example 01: Expand (a + b)2 Solution: Expanding Binomially (a + b)2 = 2C0a2 + 2C1a2-1b1 + 2C2b2 (a + b)2 = (1)a2 + (2)a1b1 + (1)b2 (a + b)2 = a2 + 2ab+ b2 Note: (a – b)2 = a2 – 2ab+ b2 Example 02: Expand (a + b)3 Solution: Expanding Binomially (a + […]
Science > Mathematics > Algebra > Logarithms > Use of Laws of Logarithms Set – III In the last article, we have studied to solve problems on the use of laws of logarithms to prove given logarithmic expression. In this article, we shall study to solve more problems on these laws to prove given relation […]
Science > Mathematics > Algebra > Logarithms > Laws of Logarithm In this article, we shall study the laws of logarithm and their proofs. Laws of logarithm are very important in mathematics and every student should have confidence in using them. Laws of Product: loga(mn) = logam + logan, where a, m, n are positive […]
Science > Mathematics > Algebra > Logarithms > Concept of Logarithm In this article, we shall study the concept of logarithms and interconversion between exponential form and logarithmic form. Laws of Indices: am × an = am + n am ÷ an = am – n (a ≠ 0) (am)n = amn […]
Science > Mathematics > Algebra > Logarithms > Use of the Laws of Logarithms Set – I In the last article, we have studied the laws of logarithms and their proofs. In this article, we shall study to solve problems on laws of logarithms (law of product, Law of quotient, Law of exponent, etc.) to […]
Science > Mathematics > Algebra > Logarithms > Problems Based on Definition of Logarithms In the last article, we have studied the concept of logarithm and interconversion between exponential form and logarithmic form. In this article, we shall study to solve problems based on the definition of logarithm. Definition of Logarithm: If m = ax, […]
Science > Mathematics > Algebra > Logarithms > Use of Laws of Logarithms Set – V (Solve for x) In the last article, we shall study problems based on the change of base rule. In this article, we shall study the use of definition and the laws of logarithms to find the value of ‘x’ […]