Final answer:
To solve the inequality (130n)⁵ > n¹00 > 200 for positive integers n, we can simplify the expression and solve the resulting inequality step-by-step.
Step-by-step explanation:
In order to solve the inequality (130n)⁵ > n¹00 > 200, we need to find the range of values for positive integers n that satisfy the condition. Let's break it down step-by-step:
- Start by simplifying the expression (130n)⁵. This can be rewritten as (130⁵)(n⁵) since powers distribute over multiplication.
- Next, simplify further by calculating (130⁵) to get a constant value.
- Now, we have (constant)(n⁵) > n¹00 > 200. Since we want to find positive integers n, we can divide both sides of the inequality by n⁵.
- This gives us a new inequality: (constant) > (n¹00/n⁵) > (200/n⁵).
- Finally, we can simplify and solve this inequality to find the range of values for n.