# What are common mistakes students make with common log?

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 $x \le 0$, the domain for the inverse function (our common log) is $0 < x < \infty$