(-3/4)^3x-1=-27/64

2 min read Jun 16, 2024

Solving the Equation (-3/4)^(3x-1) = -27/64

This article will guide you through solving the equation (-3/4)^(3x-1) = -27/64. We will utilize the properties of exponents and logarithms to find the value of x.

1. Expressing Both Sides with the Same Base

First, we need to express both sides of the equation with the same base. Notice that -27/64 can be written as (-3/4)^3.

Now, our equation becomes: (-3/4)^(3x-1) = (-3/4)^3

2. Equating the Exponents

Since the bases are the same, we can equate the exponents:

3x - 1 = 3

3. Solving for x

Now, we have a simple linear equation. Let's solve for x:

3x = 4
x = 4/3

Therefore, the solution to the equation (-3/4)^(3x-1) = -27/64 is x = 4/3.

Conclusion

By using the properties of exponents and simplifying the equation, we were able to find the solution for x. It's important to remember that when working with exponents, it's often helpful to express both sides of the equation with the same base to simplify the process.