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

1. Feb 9, 2013

### xeon123

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?

2. Feb 9, 2013

### phinds

Have you tried it on some values? Do you get the same results?

3. Feb 9, 2013

### Vorde

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 $\sqrt{x}= e^\frac{\ln{x}}{2}$

4. Feb 10, 2013

### xeon123

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

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

Last edited: Feb 10, 2013
5. Feb 10, 2013

### Vorde

Yes, just the definition of logs.

6. Feb 10, 2013

### Staff: Mentor

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.