# Is $x = - lo{g_2}(x)$ a complex number

1. Jun 5, 2012

### friend

If I have a function such that $x = - lo{g_2}(x)$, then must x be a complex number? Thanks.

2. Jun 5, 2012

### D H

Staff Emeritus
There are complex solutions to this, but there is one solution that is real.

3. Jun 5, 2012

### haruspex

At x = 1, LHS is the larger; at x = 1/2, RHS is the larger. Since both functions are continuous in that range, there must be a real solution between the two.

4. Jun 5, 2012

### D H

Staff Emeritus
That's the number I was thinking of.

5. Jun 6, 2012

### xAxis

also, it is an equation, not a function