Isn't square root a bit like Log()?

I want start by saying that my math skills aren't great and I'm trying to learn.

I took a look at square root.

Squaring the number means x^2.

And if I understood the square root correctly it does a bit inverse of squaring a number and gets back the x.

I had a friend tell me a while ago that Log() is also opposite of exponent, wouldn't that mean that square root is like a variant of Log() that only inverse a squared number?

Solution 1:

It might be best to answer with some examples.

• The number $\log_7 23$ answers the question $7^{?} = 23$.

• The number $\sqrt[7]{23}$ answers the question $?^7 = 23$.

As you can see, these are different questions.

Some further points:

• When we write $\log$, this is short for $\log_{10}$. So the number $\log 23$ answers the question $10^? = 23$.

• When we write $\sqrt{\phantom{x}}$, this is short for $\sqrt[2]{\phantom{x}}$. So the number $\sqrt{23}$ answers the question $?^2 = 23$.