Solve Exponential Inequalities

Solve the inequalities.

(1) 6(5 - 1.6^(x) greater than or equal to 13

(2) 4^(5 - x) > 15

(1)
6(5 - 1.6^x)) ≥ 13
5 - 1.6^x ≥ 13/5
1.6^x ≤ 5 - 13/5
1.6^x ≤12/5
x log(1.6) ≤ 2.4
log(1.6) > 0, dividing by log(1.6):
x ≤ log(2.4)/log(1.6)

(2)
4^(5 - x) > 15
(5 - x) log(4) > log(15)
5 - x > log(15)/log(4)
x < 5 - log(15)/log(4)

1) 6(5 - 1.6^(x) >/= 13
5 - 1.6^x >/= 13/6
-1.6^x >/= 13/6 - 5
-1.6^x >/= -17/6
1.6^x log_1.6 (1.6^x) x x
2) 4^(5 - x) > 15
log_4 [ 4^(5 - x) ] > log_4 (15)
5 - x > log_4 (15)
-x > log_4 (15) - 5
x < 5 - log_4 (15)
x < 3.0466