Logbcos
Logbcos is the notation for the function f(x) = log_b(cos x), the logarithm of the cosine of x with base b. In this form, log_b denotes the logarithm with base b, a function defined for positive bases b ≠ 1.
For real-valued outputs, the argument of the logarithm must be positive, so cos x > 0. The domain
The derivative is f'(x) = (-sin x)/(cos x ln b) = -(tan x)/ln b, provided cos x ≠ 0.
The range depends on the base b. If b > 1 (ln b > 0), then cos x ∈ (0,1],
Examples: f(0) = log_b(1) = 0, while f(π/3) = log_b(1/2) < 0 for b > 1. In programming contexts, logbcos may
See also: logarithms, trigonometric functions, log_b of positive arguments.