Logarithm

A logarithm is the exponent to which a base must be raised to produce a given number. In other words, it is the inverse operation to exponentiation. The logarithm of a number x with base b is denoted as log_b(x).

Properties of Logarithms:

1. Product Rule: log_b(mn) = log_b(m) + log_b(n)
2. Quotient Rule: log_b(m/n) = log_b(m) - log_b(n)
3. Power Rule: log_b(mⁿ) = n * log_b(m)
4. Change of Base Formula: log_b(x) = log_a(x) / log_a(b)

Common Logarithms and Natural Logarithms:

The common logarithm has a base of 10 and is denoted as log(x). The natural logarithm has a base of the mathematical constant e (approximately 2.718) and is denoted as ln(x).

Applications of Logarithms:

Logarithms are used in various fields such as finance, population growth, earthquake measurement (Richter scale), and signal processing.

Study Guide:

• Understand the definition of a logarithm and how it relates to exponentiation.
• Practice applying the properties of logarithms, including the product, quotient, and power rules.
• Be familiar with common logarithms (base 10) and natural logarithms (base e).
• Work on real-world problems that involve the use of logarithms to gain practical application skills.

Remember to practice solving various logarithmic equations and applying logarithmic functions to real-world scenarios to strengthen your understanding of this topic.