log100

Log100 refers to the logarithm with base 100, typically written as log base 100 of x, or log_100(x). It is defined for positive real numbers x and is the exponent y that satisfies 100^y = x. Because the base 100 is greater than 1, log_100(x) is a strictly increasing function on x > 0.

Key values and scaling

- log_100(100) = 1, since 100^1 = 100.

- log_100(1) = 0, since 100^0 = 1.

- log_100(0.01) = -1, since 100^-1 = 0.01.

A useful scaling property is that multiplying x by 100 increases log_100(x) by 1; multiplying x by 10 increases log_100(x) by 0.5.

Change of base and relations

Logarithms with base 100 can be computed via the change-of-base formulas:

log_100(x) = log_10(x) / log_10(100) = log_10(x) / 2, or equivalently log_100(x) = ln(x) / ln(100).

Thus log_100(x) is exactly half of the common logarithm log_10(x).

Graph and interpretation

The graph of log_100(x) is a smooth, increasing curve defined for x > 0, passing through (1, 0) and (100, 1). As x grows by a factor of 100, the value of log_100(x) increases by 1.

Applications and notes

Log_100 is less common than logarithms with bases 2, e, or 10, but it can appear in contexts requiring a base-100 scale or in theoretical discussions of logarithmic bases. In practical calculations, it is often convenient to use the change-of-base relation to compute log_100(x) from standard log functions.