The complex dielectric constants of binary mixtures of water-methanol and water-ethanol in the frequency range from 45 MHz to 26.5 GHz, and binary mixtures of methanol-ethanol in the range from 200 MHz to 26.5 GKz have been measured with various volume fractions around room temperature by means of an open-ended coaxial sensor and a network analyzer. Methanol-ethanol mixtures display a near-Debye dispersion while water-alcohol mixtures show a Cole-Davidson dispersion. The logarithm of relaxation time log tau and dielectric decrement Delta epsilon for methanol-ethanol mixtures show a good linear relation with the volume fraction of methanol, while log tau and Delta epsilon extracted with the Debye function for water-alcohol mixtures display a near-linear relation with volume fraction of water. Two simple formulas are proposed for identifying the volume fractions of the components in binary mixtures of alcohol-alcohol and water-alcohol from a knowledge of tau and Delta epsilon for the pure liquids and the mixtures. The validity of these formulas has been demonstrated with three blind tests. The relation between the mole fraction of water and log tau for water-methanol and water-ethanol mixtures extracted by the use of a Cole-Davidson function clearly shows two linear regions, which implies a change of relaxation mechanism with mole fraction.