Logarithms are necessary to handle quantities spanning billions in range

Evidence

Whenever a quantity can vary by factors of millions or billions and yet be of significance over its whole range, we need to bring logarithms to the rescue. The logarithm measures the exponent that gives the number. The base of the logarithm is the number we are raising to a power, and the power is the logarithm of the number. Thus, by definition 7.3485 = 10log10(7.3485). (We write the base as a subscript on the log.) By trial and error if need be (but of course we now have computers and before that, log tables), you can show that 7.3485 = 100.866199, or log10(7.3485) = 0.866199. — Eric J. Heller, Why You Hear What You Hear- An…, 223

Categorization

• DEFINE: Explains the log scale concept that underpins the decibel system for sound intensity.