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

1 Answer
Aug 8, 2018

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]}