We're glad you stopped by Solve the equation 5n 4 3 frac 1 125 The solution set is A frac 1 25 B frac 1 25 C frac 1 5. This page is here to walk you through essential details with clear and straightforward explanations. Our goal is to make your learning experience easy, enriching, and enjoyable. Start exploring and find the information you need!
Answer :
Isolating n and taking the fourth root of both sides (considering positive/negative solutions) leads to n = ±0.2. Since 5^(1/3) is positive, 5n^4/3 is positive only when n is positive. Converting the decimal solution (0.2) to a fraction gives n = 1/5.
Option c.
The correct answer is:
c) (1/5)
Here's how to solve the equation:
Isolate n:
Multiply both sides by 125 to get rid of the denominator on the right.
Simplify the resulting equation:
5n^4/3 × 125 = 1/125 × 125
125n^4 / 3 = 1
Simplify further:
Multiply both sides by 3 to get rid of the fraction on the left.
125n^4 = 3
Take the fourth root of both sides:
Important Note: Taking the fourth root of an equation can result in positive and negative solutions, so we need to consider both possibilities.
n = ±(∛(3 / 125))
Calculate the solutions:
n = ±(∛(0.024)) ≈ ±(0.2)
Solutions:
Therefore, the solution set for the equation is:
n = {0.2, -0.2}
However, the question asks for a single answer that represents the correct solution. In this case, since 5^(1/3) is a positive value (approximately 1.7), raising it to the power of 4 will always result in a positive number. So, the only valid solution that satisfies the original equation is:
n = 0.2
However, the answer choices only provide values as simplified fractions. Converting the decimal solution (0.2) to a fraction, we get:
n = 1/5
Therefore, the correct answer based on the available options is (c) (1/5).
Option c.
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