Pure: Indices and Logarithms

A. Indices (Exponents) Definition: An index (or exponent) indicates how many times a base number is multiplied by itself. Explanation: When you see a number like 2³, the '2' is the base and the '3' is the index. It means you multiply 2 by itself 3 times (2 × 2 × 2). Indices provide a shorthand way to write repeated multiplication, making large numbers or complex expressions easier to manage. Understanding indices is fundamental for solving many mathematical and scientific problems. Think of it as: Think of indices like stacking blocks. If you have a base block and an index of 3, you stack 3 identical blocks on top of each other. The total height represents the value of the expression. Real-world application: Indices are used in calculating compound interest, where the principal amount grows exponentially over time. For example, if you invest money at 5% interest compounded annually for 10 years, the final amount involves a calculation like (1.05)¹0. B. Logarithms Definition: A logarithm is the power to which a base must be raised to produce a given number.