# Log base 2 is the same thing as square root?

Hi,

Is is correct to say that the logarithm of base 2 of a number x, is the same thing as the square root of a number x?

## Answers and Replies

phinds
Gold Member
2019 Award
Have you tried it on some values? Do you get the same results?

No, not at all.

To say that ##\log_2{x} = y## you mean that ##x=2^y##, logarithms are just ways of 'inversing' exponentiation (roughly). To say that ##\sqrt{x}=y## you are saying that ##x = y^2##, completely different.

However, there is a neat little tidbit that says that ##\sqrt{x}= e^\frac{\ln{x}}{2}##

Ok. But I can say that these 2 expressions are correct?

$\log_{b} x = y$, and $b^y=x$

Last edited:
Yes, just the definition of logs.

Mark44
Mentor
Ok. But I can say that these 2 expressions are correct?

$\log_{b} x = y$, and $b^y=x$
The appropriate terminology is that the two equations are equivalent. This means that any ordered pair (x, y) that satisfies one equation also satisfies the other. It also means that both equations have the same graph.