Complete answer with "simple" operators (+, -, *, /, ⁰, ², ³, !, log):
(10 + 10) / (10 + 10) = 1
(10 / 10) + (10 / 10) = 2
(10 + 10 + 10) / 10 = 3
((10 / 10) + (10 / 10))² = 4
Another one : log(10) + log(10) + log(10) + log(10) = 4
(10 * 10) / (10 + 10) = 5
((10 + 10 + 10) / 10)! = 6 (thanks to Kepotx)
10 - 10⁰ - 10⁰ - 10⁰ = 7 (thanks to Stefano Lonati)
Another one : 10 - log(10 * 10 * 10) = 7 (thanks to Stefano Lonati)
((10 / 10) + (10 / 10))³ = 8
Another one : 10 * log(10) - log(10) - log(10) = 8 (thanks to Stefano Lonati)
((10 * 10) - 10) / 10 = 9
10 + (10 - 10) * 10 = 10