logaritmfunktsioon

The logarithmic function, often denoted as log or ln, is the inverse of the exponential function. For a base 'b' greater than zero and not equal to one, the logarithmic function y = log_b(x) answers the question: "To what power must 'b' be raised to equal 'x'?" In other words, if b^y = x, then y = log_b(x).

The most common bases for logarithmic functions are base 10, denoted as log(x) or log10(x), and the natural base 'e' (approximately 2.71828), denoted as ln(x) or log_e(x). The natural logarithm is particularly important in calculus and many areas of science.

The domain of a logarithmic function is all positive real numbers (x > 0), as you cannot take the logarithm of zero or a negative number. The range of a logarithmic function is all real numbers.

Key properties of logarithms include the product rule (log_b(xy) = log_b(x) + log_b(y)), the quotient rule (log_b(x/y) = log_b(x) - log_b(y)), and the power rule (log_b(x^p) = p * log_b(x)). These properties allow for the simplification and manipulation of logarithmic expressions.

Logarithmic functions are used in various fields, including measuring earthquake intensity (Richter scale), sound loudness (decibels), and acidity (pH scale). They also appear in algorithms, finance, and statistics.