1) (√6)^x ≤ 36
√6^x ≤ 36
6^x ≤ 36^2
6^x ≤ 1296
x*log(6) ≤ log(1296)
x ≤ log(1296) / log(6)
x ≤ 4

2) 6^(x+1) >= 1/6
6^x 6^1 >= 1/6
6^x 6 >= 1/6
6^x >= 1/36
x*log(6) >= log(1/36)
x >= log(1/36)/log(6)
x >= -2

Отже, розв'язком буде:
1) x ≤ 4
2) x >= -2