Learn: Logarithms and Natural Logarithms

Welcome!Today we'll explore logarithms and natural logarithms. This lesson is designed to help you understand their purpose and how to work with them step by step.

What Are Logarithms?A logarithm is the inverse operation of exponentiation. It helps you find the power to which a base number must be raised to produce a given number. For example, log2(8) = 3 because 23 = 8.

Natural LogarithmsNatural logarithms use the base e, where e is approximately 2.718. They are written as ln(x) and are widely used in mathematics and science, especially for growth and decay problems.

Why Are Logarithms Useful?Logarithms simplify calculations involving large numbers. For example, they are used in measuring sound intensity (decibels) and earthquake magnitudes (Richter scale).

Rules of LogarithmsThere are several key rules: product rule (logb(x × y) = logb(x) + logb(y)), quotient rule (logb(x ÷ y) = logb(x) - logb(y)), and power rule (logb(xn) = n × logb(x)).

Change of Base FormulaThe change of base formula allows you to calculate logarithms with any base: loga(x) = logc(x) ÷ logc(a). It's often used with base 10 or e.

Review Time!Great work! You've learned about logarithms, natural logarithms, their rules, and the change of base formula. Let's check your understanding with a few questions.