Making X the Subject of the Formula y x^b / x^a

Introduction

In algebra, it is often necessary to manipulate equations to express a variable in terms of others. This process, known as solving for a specific variable, is crucial in many areas of mathematics and its applications. In this article, we explore how to transform the equation y xb / xa to have x as the subject.

Step-by-Step Solution

Let's consider the equation y xb / xa (where x not equal to a):

tFirst, we multiply both sides of the equation by xa: t

y xa xb

t tNext, we rewrite the equation by distributing the multiplication:

t

xya - xa b - ay

t tThen, we collect all the terms involving x on one side of the equation:

t

xya - xa b - ay

t tFactor out x from the left-hand side:

t

x(ya - 1) b - ay

t tFinally, we solve for x by dividing both sides by (ya - 1) (assuming ya - 1 ≠ 0): t

x (b - ay) / (ya - 1)

t

Therefore, the final expression is:

x (b - ay) / (ya - 1)

Conclusion

This process demonstrates the step-by-step method of transforming an equation to have a desired variable as the subject. It is a fundamental skill in algebra and is used extensively in various fields such as physics, engineering, and economics. Understanding these transformations is crucial for solving complex problems and expressing relationships between variables clearly.

By following these steps, you can solve for x in similar equations, providing a valuable skill set for your mathematical toolkit.