A logarithm is the power to which a base must be raised to produce a given number. It's the inverse operation of exponentiation.
Types of Logarithms:
- • Common (log): Base 10, used in engineering
- • Natural (ln): Base e, used in calculus
- • Binary (log₂): Base 2, used in computer science
- • Custom Base: Any positive base ≠ 1
Key Properties:
- • log_b(xy) = log_b(x) + log_b(y)
- • log_b(x/y) = log_b(x) - log_b(y)
- • log_b(x^n) = n × log_b(x)
- • log_b(b) = 1, log_b(1) = 0
Applications:
- • pH calculations in chemistry
- • Decibel measurements in acoustics
- • Earthquake magnitude (Richter scale)
- • Algorithm complexity analysis