Is [itex]x = - lo{g_2}(x)[/itex] a complex number

[friend]

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

 

[D H]

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

 

[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.

 

[D H]

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.

That's the number I was thinking of.

 

[xAxis]

also, it is an equation, not a function