Decimal Logarithm: Definition and Properties

The page introduces the concept of the decimal logarithm and its fundamental properties. The decimal logarithm, denoted as 'log', is a crucial function in mathematics and various scientific disciplines.

Definition: The decimal logarithm function (log) is defined on the interval (0, +∞) and is the reciprocal of the power of ten function.

This definition establishes the relationship between logarithms and exponents, which is essential for understanding logarithmic operations.

Example: The reciprocal nature of log and power of ten is demonstrated by the equations: log(10ˣ) = x and 10^(log(x)) = x.

The page then outlines several key properties of logarithms:

Highlight: Important properties of logarithms include:

1. log(1) = log(10⁰) = 0
2. log(10) = log(10¹) = 1
3. log(a × b) = log(a) + log(b)
4. log(a/b) = log(a) - log(b)
5. log(aᶜ) = c × log(a)

These properties form the foundation for solving more complex logarithmic equations and are essential for manipulating logarithmic expressions.

Vocabulary: The term "réciproque" used in the French text translates to "reciprocal" or "inverse" in English, referring to the inverse relationship between the logarithm and exponential functions.

Understanding these properties is crucial for students studying advanced mathematics, physics, or chemistry, as logarithms play a significant role in various scientific calculations and problem-solving scenarios.