loga100001

loga100001 is a mathematical notation commonly read as log base a of 100001. In standard notation it is written log_a(100001). The value represents the exponent to which the base a must be raised to produce 100001.

The logarithm is defined for positive numbers with a base a where a > 0 and a ≠ 1. It satisfies a^{log_a(100001)} = 100001 and log_a(100001) = ln(100001)/ln(a), where ln denotes the natural logarithm. This relation shows how the base affects the magnitude of the result.

If the base a is greater than 1, log_a(x) is an increasing function of x; if 0 < a < 1, it is decreasing. The domain is x > 0 and the range is all real numbers. For any base, log_a(1) = 0 and log_a(a) = 1.

Numerical examples: with a = 10, log_10(100001) ≈ 5.0000043. With a = e, log_e(100001) = ln(100001) ≈ 11.5129. With a = 1/2, log_{1/2}(100001) ≈ -16.6.

Notation can be ambiguous in non-mathematical contexts. Some texts and programming languages use different conventions for representing logarithms, such as log(x) for a default base or log_b(x) with explicit base. When the base is not stated, the meaning should be inferred from context.