Question

Math

Posted 4 months ago

`What is the smallest positive integer solution to $\left(\frac{100,000,000}{x^{4}}\right)<1$ ?`

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 1

To find the smallest positive integer solution, we start by solving the inequality $\left(\frac{100,000,000}{x^{4}}\right)<1$

step 2

Multiply both sides of the inequality by $x^4$ to get $100,000,000 < x^4$

step 3

Take the fourth root of both sides to find $x > \sqrt[4]{100,000,000}$

step 4

Calculate the fourth root of 100,000,000 to get $x > 100$

step 5

Since we are looking for the smallest positive integer solution, the answer is the smallest integer greater than 100, which is 101

Answer

101

Key Concept

Solving Inequalities Involving Powers

Explanation

To solve the inequality, we isolated the variable by multiplying both sides by $x^4$ and then took the fourth root to find the range of solutions. We then identified the smallest integer greater than 100 to find the smallest positive integer solution.

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