A logarithm is a mathematical function that plays a key role in various scientific and mathematical applications. It serves as the inverse operation to exponentiation.

Understanding Logarithms:

The logarithm of a number is the exponent to which a fixed base must be raised to produce that number.

It answers the question: "To what power must the base be raised to obtain a certain number?"

Common Bases in Logarithms:

The most commonly used bases for logarithms are 10 (common logarithm) and e (natural logarithm, where e ≈ 2.71828).

The logarithm to base 10 is denoted as log, and the logarithm to base e is denoted as ln.

Formula of Logarithm:

The logarithm of a number x with base b is denoted as log_b(x).

It is defined such that if y = log_b(x), then b^y = x.

Example:

To find the logarithm of 100 to base 10:

log_10(100).

Since 10^2 = 100, log_10(100) = 2.

Key Points to Remember:

Logarithms transform multiplicative processes into additive ones, which simplifies complex calculations.

They are used in exponential growth or decay problems, sound intensity measurements, and in understanding scales of seismic activity.

**© 2023 AI MATH COACH**