Domain of f(x) = log₅(log₅(x + 2))

[the_storm]

The Question is: What is the Domain of the function f(x)= log$$_{5}$$(log$$_{5}$$(x + 2)
My answer is that the Domain is (-2, $$\infty$$). However the it is said that the right answer is (-1, $$\infty$$) and I am not convinced so can anyone give me an explanation?

 

[micromass]

You can't take logs of negative numbers. So you'll need to make sure that

$$x+2\geq 0$$

But there's another log in that formula. That log also can't take negatives as input. So moreover, you'll have to make sure that

$$\log^5(x+2)\geq 0$$

 

[the_storm]

so Domain is (-1, infinty) right??

 

[micromass]

Yes!

 

[dimitri151]

Just nitpicking to pass the morning. It's not just negative numbers you can't take the log of. It's also zero. You can't take the log of a non-positive number. No?

 

[JCVD]

You cannot take the log of zero.

 

[Landau]

If we are nitpicking: "the domain" of a function is part of the definition of that function. OP is asking for the largest possible domain that is compatible with the given formula.

 

[dimitri151]

It's true Landau, but nobody disputed that.

 

[ayuk]

can you be more explicit