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#
