Is zero a discrete logarithm?

Question

In the book Discrete Mathematics and Its Application, it said "Suppose that p is prime and r is a primitive root modulo p. If a is an integer between 1 and p-1, that is, a nonzero element of $\mathbb Z_p$, we know that there is an unique exponent e such that r^e = a in $\mathbb Z_p$, that is, r^e mod p = a."
We known 2 is a primitive root modulo 11. 2⁰=1 and 2¹⁰=1, we can see 0 and 10 both belong to $\mathbb Z$₁₁ and it isn't unique that 2^e mod 11 = 1 with e in $\mathbb Z$₁₁.
How should I understand it?