Mathematicians reserve unadorned "log" for the natural logarithm, having little use for other bases. Scientists and engineers use "log" for base 10 and require "ln" for the natural log; "lg" is base 2, especially in computer science.
The decibel scale is logarithmic, defined as log base 10, but then multiplied by 10. Essentially this is base 10^(1/10) ~= 1.25892541179.
Suppose you have some calculator with a log key, but you don't know what base it's in -- can you find the logarithm of x with respect to a particular base b? This is easy -- just key in (log x)/(log b).
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