Grade 12 · Mathematics
Logarithms
Why it matters
Inverse of exponentials.
Advanced20m readingPrerequisite: Exponential functions
What is a logarithm?
Short answer
A logarithm is the inverse of exponentiation: log_b(x) answers the question "to what power must the base b be raised to get x?" So log_b(x) = y means bʸ = x. Logarithms turn multiplication into addition and let you solve equations where the unknown is an exponent, such as exponential growth and decay problems.
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Frequently asked questions
- What is the relationship between logarithms and exponents?
- They are inverse operations: log_b(x) = y is exactly the same statement as bʸ = x.
- What is the natural logarithm?
- The logarithm with base e (≈ 2.718), written ln(x); it appears throughout growth, decay, and calculus.