log10RcRb

log10RcRb refers to the common logarithm (base 10) of the ratio of two positive quantities Rc and Rb, typically written as log10(Rc/Rb). The value is dimensionless and is equal to log10(Rc) − log10(Rb). Because logarithms convert multiplication into addition, this expression also satisfies log10(Rc/Rb) = log10 Rc − log10 Rb.

Key properties include: the function is increasing in Rc and decreasing in Rb; if Rc = Rb, the value is zero; if Rc > Rb the result is positive, and if Rc < Rb the result is negative. Multiplying both Rc and Rb by the same positive factor k leaves log10(Rc/Rb) unchanged: log10((k Rc)/(k Rb)) = log10(Rc/Rb).

Computation examples help illustrate the meaning. If Rc = 10 kΩ and Rb = 1 kΩ, log10(Rc/Rb) = log10(10) = 1. If Rc = 1 kΩ and Rb = 10 kΩ, log10(Rc/Rb) = log10(0.1) = −1.

In practice, log10RcRb is used to compare relative magnitudes on a logarithmic (base-10) scale. In electronics, resistor ratios expressed in this way can inform qualitative assessments of gain or bias in simplified analyses, while in data analysis it serves to compare ratios on a compact, interpretable log scale. See also: logarithm, log10, ratio, resistor.