Solve the inequality 16^(x-1)>2^(2x+2)

We'll write both bases as power of
2:

2^4(x-1)>2^(2x+2)

Since
the bases are bigger than unit value, the function is increasing and we'll
get:

4(x-1)> 2x+2

We'll
divide by 2:

2(x- 1) > x +
1

We'll remove the
brackets:

2x - 2 > x +
1

We'll subtract x both
sides:

2x - x - 2 > 1

x
- 2 > 1

We'll add 2 both
sides:

x > 2 + 1

x
> 3

The interval of values of x, for
the inequality holds, is (3 , +infinite).