), as logarithms of zero or negative numbers are undefined in the real number system . 2. Essential Logarithmic Rules

The mathematical relationship between an exponential form and a logarithmic form is:

According to the Math Centre , logarithms follow specific laws that mirror exponent rules: : Quotient Rule : Power Rule : Identity : Zero Rule : 3. Common vs. Natural Logarithms Common Logarithm (

A logarithm is the of an exponential function. In simple terms, it asks the question: "To what power must we raise a base to get a certain number?" For example, the logarithm base 10 of 1,000 is 3 , because 1. Fundamental Definition

) : Logarithm with base 10 . If no base is written, base 10 is usually implied. : Logarithm with base ≈2.718is approximately equal to 2.718 ). This is critical for modeling natural growth and decay. 4. Graphing Logarithmic Functions Solving Logarithmic Equations (5 Examples)

by=x⟺logb(x)=yb to the y-th power equals x ⟺ log base b of x equals y (Base) : Must be positive and not equal to 1. (Argument) : Must be positive (