Which of the following statements is true regarding decibels?

The statement that decibels involve a ratio and a logarithm is accurate and highlights the fundamental nature of how decibels are used to express sound intensity. Specifically, the decibel scale is logarithmic, meaning it represents the logarithm of the ratio of a particular sound pressure level to a reference level. This is important because the human ear perceives sound intensity in a nonlinear fashion; thus, the logarithmic scale allows for more manageable comparisons of sound levels across a wide range of intensities.

For instance, an increase of 10 dB corresponds to a tenfold increase in sound intensity, which effectively conveys the exponential nature of sound pressure changes in relation to human perception. This logarithmic approach allows for a more practical understanding of sound levels that can vary significantly, as opposed to a direct linear measurement which would not adequately reflect the vast differences in perceived loudness. Hence, the significance of this characteristic makes option three the correct choice regarding decibels.