# How do you evaluate (log_(10)x)^2?

There's not much to say. If we are given a number, we can solve this. For example, if $x = 100$,
${\left({\log}_{10} \left(100\right)\right)}^{2} = {2}^{2} = 4$
We know the zero of this function is still $x = 1$. We know that the domain of the function is $x \in \left(0 , \infty\right)$. The range is obviously also $\left[0 , \infty\right)$, since it's like ${x}^{2}$ still.
We could imagine sketching from these properties alone. For low values, this blows up (since log of a number near 0 is a large negative). It is well known that $\log$ grows far more slowly than $x$, so we expect this to be similar to a log function with a little more life: