Page 2: Properties of Logarithms
This page delves into the proprietà dei logaritmi, which are crucial for solving logarithmic equations and simplifying expressions.
Key properties include:
- log_a 1 = 0
- log_a a = 1
- a^logab = b
Vocabulary: The logaritmo definizione matematica states that logarithms and exponentials are inverse functions.
The page introduces three important rules:
- Logarithm of a Product: log_a b∗c = log_a b + log_a c
- Logarithm of a Quotient: log_a b/c = log_a b - log_a c
- Logarithm of a Power: log_a bm = m * log_a b
Example: log_2 8∗4 = log_2 8 + log_2 4 = 3 + 2 = 5
The page concludes with the change of base formula, which allows conversion between logarithms of different bases:
log_a b = logcb / logca
This formula is particularly useful when using calculators, as most support only natural basee or common base10 logarithms.