A logarithm is the mathematical inverse of exponentiation. It answers the question: To what power must a given base be raised to produce a specific number? [1, 2]
For example, since 2³ = 8, the logarithm of 8 with base 2 is 3. [2]
The Core Equation
A logarithmic equation is written as: $\log_b(x) = y \quad \text{if and only if} \quad b^y = x$
Where:
- b: The base of the logarithm (must be a positive number and not equal to 1).
- x: The argument (the resulting number).
- y: The logarithm itself (the exponent to which b is raised). [3, 4]
Common Types of Logarithms
- Common Logarithm: Uses base 10 and is usually written simply as $\log(x)$ (e.g., $\log(100) = 2$ because 10² = 100).
- Natural Logarithm: Uses base e (an irrational mathematical constant approximately equal to 2.71828) and is written as $\ln(x)$.
- Binary Logarithm: Uses base 2 and is widely used in computer science and information theory. [5, 6, 7, 8, 9]
Explore logarithmic equations, properties, and calculation rules through resources like BYJU'S Logarithmic Functions or GeeksforGeeks Log in Maths.
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