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

by xeon123
Tags: base, root, square, thing
 P: 78 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?
 PF Patron P: 4,951 Have you tried it on some values? Do you get the same results?
 P: 781 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}##
P: 78

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

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

$\log_{b} x = y$, and $b^y=x$
 P: 781 Yes, just the definition of logs.
Mentor
P: 19,710
 Quote by xeon123 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.

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