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

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to solve the inequality 16^(x-1)>2^(2x+2)

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

We convert 16 to 2 to the power 4

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

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

As 2 is positive 4x - 4 > 2x + 2

=> 2x - 2 > x + 1

=> x > 3

The value of x > 3 satisfy the inequality.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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).

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