Perhaps the most common mistake made with the common log is simply forgetting that one is dealing with a logarithmic function.
This in and of itself can lead to other mistakes; for example, believing that log y being one greater than log x means that y is not much larger than x. The nature of any logarithmic function (including the common log function, which is simply log_10) is such that, if log_n y is one greater than log_n x, that means that y is greater than x by a factor of n.
Another common error is forgetting that the function does not exist for values of x equal to or less than 0. The result of the common log function is simply the variable y for the equation x = 10^y. As there is no value for y (in the domain of real numbers) for which x<=0, the domain for the inverse function (our common log) is 0 < x < oo
