What is the meaning of $\log^2n$ and how should it be read in word form?

Question

$\log^2n$ is what I need assistance with. How is this read in word form?

What exactly does this mean? No matter how much I read about logarithms, they still seem new to me.

Answer 1

$\log(x)$ is a function.

Generally, the default is to use the natural logarithm or $\ln(x) = \log_e(x)$, but it is not unnatural in some settings to think of $\log(x)$ as base $10$.

The function generates a number that represents what power the base would have to be raised to to equal x. In other terms, $ log_a(x) = b $ where $a^b = x$.

For example, $2^3 = 8$, so $log_2(8) = 3$.

Finally, $\log^2(x) = (\log(x))^2$, which is just the square of the function.

Answer 2

It is essentially the square of $\log n$. Just like $\sin^2\theta$ is $(\sin\theta)^2$, $\log^2n:=(\log n)^2$. Simply read it as "log squared of n".

Answer 3

You could probably read it just about anyway you want. But, I am assuming this is the square of the Log of n so I would read it as "Log n squared" noting of course that this is slightly ambiguous. Another way would be to say "log squared n" which is OK as it sounds similar to something like $\sin^2x$.