Question

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

Answer 1

There's not much to say. If we are given a number, we can solve this. For example, if `x = 100`,
`(log_10(100))^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 (0, infty)`. The range is obviously also `[0, infty)`, 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:
graph{log(x)^2 [-1, 20, -1, 2]}